BRENNAN, Circuit Judge. An airline agent was terminated after she abused her travel privileges. She sued, claiming she was harassed because of her race and fired in retaliation for reporting the harassment. The airline maintains it properly handled her complaints and that she was dismissed for just cause.

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The district court granted the airline summary judgment, denied the agent’s motion to alter or amend that judgment, and ordered the agent to pay the airline’s costs. We affirm each of these decisions. I In reviewing a grant of summary judgment, we construe all facts and draw all inferences in the light most favorable to the non-moving party. Pack v. Middlebury Cmty. Sch., 990 F.3d 1013, 1017 (7th Cir. 2021). Here, that is Ciara Vesey, an African American woman who began work in 2012 for Envoy Air, Inc. as a station agent at Quad Cities International Airport in Rock Island County, Illinois. Several incidents occurred during Vesey’s four years of employment with Envoy. For example, in November 2014 she drove a jet bridge into an aircraft. Vesey received a serious reprimand and signed a letter of commitment agreeing to comply with all company rules and regulations. This repri- mand—the last step before termination—was to remain in ef- fect for two years. In 2016, Vesey and other Envoy employees also lodged workplace-related complaints against each other. Beginning in February and March, Vesey complained to the airline’s hu- man resources department of favoritism and bias. Envoy in- vestigated and found her allegations unsubstantiated. But that August, Vesey reported that a coworker, Eric Masengarb, directed racist remarks and actions at her. Envoy found this complaint substantiated and fired Masengarb. Vesey also said that in 2016, one of her lead agents, Carrie McMurray, and her general manager, Teresa White—who had defended Masengarb and sought to rehire him—

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undertook a campaign of retaliation and harassment against her. McMurray lodged a complaint, which was ultimately found unsubstantiated, that Vesey had posted racist content on Facebook. McMurray also told others she did not want to work with Vesey anymore. Both McMurray and White said they wanted Vesey fired. Vesey further claims that previously missing evidence—which she says is cause for reconsidera- tion of the district court’s decision on summary judgment— shows that White pressured Ashley Emerick, another em- ployee, into filing an anonymous complaint alleging that Vesey abused her travel benefits. Envoy’s employment benefits included flying standby for free. As part of her employment, Vesey signed Envoy’s rules and regulations that specified “[a]buse of travel privileges will be grounds for dismissal.” In September 2016, Emerick complained that Vesey was abusing Envoy’s travel benefits. Envoy investigated and concluded that, numerous times throughout 2016, Vesey had abused those benefits and her ac- cess to the airline’s booking system. The company discovered that on two occasions, Vesey— although not intending to travel—had used her employee ac- cess to volunteer to receive a travel voucher in exchange for taking a later flight, which she would then cancel. The first time, other customers volunteered for the travel voucher be- fore her, hampering Vesey’s plan, so she used her employee access to the booking system to cancel her reservation five minutes before the flight was due to take off. The second time Vesey successfully collected a $500 voucher in exchange for postponing her reservation by one day. Never intending to take the trip, she then cancelled the new reservation.

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On two other occasions, Envoy’s investigators found that Vesey put herself on standby for flights for which she already held non-standby reservations. After successfully boarding the flight off the standby list, Vesey would cancel her non- standby reservation. This prevented the airline from selling a seat and improved her odds of flying standby for free. Envoy further discovered that Vesey had convinced another em- ployee to check her in for a return flight via the airline’s book- ing system when she had missed the departure flight on the same reservation. Passengers usually cannot fly only part of their reservation, so by having her co-worker manually check her in through the booking system, Vesey avoided the possi- bility of having to pay change fees. Envoy’s investigators con- cluded that all of these actions by Vesey violated company policy. Before the end of the investigation, Vesey again com- plained to human resources, claiming that McMurray was harassing and stalking her by looking at her travel history. Envoy found this complaint to be unsubstantiated, and that even if the allegations were true, they would not have amounted to improper conduct by McMurray. Given the active reprimand for the jet bridge incident, and the finding that Vesey had abused her travel benefits, the in- vestigator recommended the airline terminate her. A com- pany committee agreed, and Vesey was terminated in October 2016. II Vesey sued Envoy, alleging among other things retaliation and a hostile work environment in violation of Title VII of the Civil Rights Act of 1964 and the Illinois Human Rights Act.

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According to Vesey, Envoy’s findings against her were pre- textual, and the airline investigated and terminated her in re- taliation for her reporting racist and retaliatory conduct by other Envoy employees. Vesey also alleged that she suffered a hostile work environment due to the conduct of Masengarb, McMurray, and White. The district court granted Envoy summary judgment, rul- ing that Vesey was not terminated in retaliation for her con- duct, and that the hostility Vesey claimed she was subjected to did not constitute a racially hostile work environment. Af- ter some dispute, and with some modification, the district court also granted costs to Envoy. Following the district court’s judgment, Vesey discovered that the transcript of Emerick’s deposition she had received from the court reporter was incomplete. Specifically, the part of the transcript Vesey originally submitted to the court omit- ted Emerick’s explanation that White had pressured her to file the complaint about Vesey’s abuse of travel benefits. Vesey moved to alter or amend the judgment against her under Fed- eral Rule of Civil Procedure 59(e). She argued that the previ- ously missing portion of the deposition transcript was newly discovered evidence corroborating her allegation that her ter- mination was retaliatory. The district court ruled against her again, holding that Vesey’s lack of diligence in uncovering the mistake did not make the evidence newly discovered for pur- poses of Rule 59. Vesey now appeals the district court’s grant of summary judgment to Envoy on the retaliation and hostile work envi- ronment claims, as well as the denial of her Rule 59(e) motion. She also asks us to set aside the order granting costs to Envoy.

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III A We review a district court's grant of summary judgment de novo, construing all facts and drawing all inferences in the light most favorable to the non-moving party. Pack, 990 F.3d at 1017. Summary judgment is appropriate if there is no gen- uine dispute as to any material fact and the movant is entitled to judgment as a matter of law. FED. R. CIV. P. 56(a). To sustain a retaliation claim, Vesey must show that (1) she engaged in an activity protected by the statute; (2) she suf- fered an adverse employment action, and (3) there was a causal link between the protected activity and the adverse action. Lewis v. Wilke, 909 F.3d 858, 866 (7th Cir. 2018). For pur- poses of summary judgment, Envoy conceded that Vesey’s filing of complaints was a protected activity and that her ter- mination was an adverse employment action. The only dis- pute, then, is as to the causal link. Vesey does not allege retaliatory motives by Envoy’s in- vestigators who recommended her termination, or by the committee members who approved it. Instead, she argues that Envoy is liable under a cat’s paw theory of liability. This theory applies when a biased supervisor “who lacks decision- making power uses the formal decision maker as a dupe in a deliberate scheme to trigger a discriminatory employment ac- tion.” Johnson v. Koppers, Inc., 726 F.3d 910, 914 (7th Cir. 2013) (internal quotation marks omitted). Vesey claims that White harbored retaliatory animus and encouraged Emerick to file the anonymous complaint against her. But the mere fact that an employee’s wrongdoing was re- ported by a biased supervisor with a retaliatory or

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discriminatory motive does not establish liability under a cat’s paw theory. Where the “investigation results in an ad- verse action for reasons unrelated to the supervisor’s original biased action … then the employer will not be liable.” Staub v. Proctor Hospital, Inc., 562 U.S. 411, 421 (2011). Rather, a plain- tiff must show that the biased supervisor’s actions were a proximate cause of the adverse employment action. Id. at 420. Proximate cause exists only if the investigation took the com- plaint “into account without determining that the adverse action was, apart from the supervisor’s recommendation, en- tirely justified” or if the investigation “relies on facts provided by the biased supervisor.” Id. at 421. 1 So, if an employer’s de- cision to take an adverse employment action did not rely on the credibility of a biased supervisor—that is, the employer believed it had independently sufficient reasons, such as cor- roboration of the allegations, to take the adverse action—then the employee’s cat’s paw theory will fail for lack of proximate cause. See Woods v. City of Berwyn, 803 F.3d 865, 870–71 (7th Cir. 2015) (when terminating employee, city board “did not rely” on the conclusions of an allegedly biased supervisor, in- stead deciding based on facts presented by an unbiased party, so cat’s paw theory of liability did not apply); accord Singh v. Cordle, 936 F.3d 1022, 1038 (10th Cir. 2019) (explaining that proximate cause for a cat’s paw theory exists when the deci- sion to take adverse action is based on “’uncritical reliance’ on facts provided by a biased subordinate”) (citation omitted).

1 This court stated in Staub v. Proctor Hosp. that “[i]t is enough that the decisionmaker is not wholly dependent on a single source of information and conducts her own investigation into the facts relevant to the decision,” 560 F.3d 647, 659 (7th Cir. 2009), but the Supreme Court rejected that standard, rev'd and remanded, 562 U.S. at 420–21 (2011).

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Here, even if Vesey’s general manager had a retaliatory motive, there is no evidence that Envoy’s investigators relied on the veracity of the complaint for anything but initiating the investigation. Indeed, the investigators said they reached their conclusion by reviewing Vesey’s travel history and ac- tivity on various airline systems and by interviewing her and the employee who had helped her modify one of her reserva- tions. No evidence presented by Vesey creates a genuine dis- pute that would allow a reasonable jury to conclude that the result of the investigation was proximately caused by the complaint rather than by the independently sufficient find- ings of Envoy’s investigation. In addition to pressing her cat’s paw theory, Vesey also argues on appeal that she did not violate any Envoy policies and that the alleged violations were therefore mere pretext for a retaliatory firing. But whether Vesey’s conduct was in fact a violation of Envoy’s company policy is beyond the scope of this case. An employer’s explanation is not pretext if “the em- ployer honestly believed in the nondiscriminatory reasons it offered.” Kellogg v. Ball State Univ., 984 F.3d 525, 528 (7th Cir. 2021) (internal quotation marks omitted). White and McMur- ray—the individuals whom Vesey claims had retaliatory ani- mus—were not proximate causes of her firing. She admits that the investigators themselves were not motivated by any discriminatory animus. And the uncontested facts about Vesey’s use of travel benefits reveal her dishonest conduct. She alleges that others were not punished for similar actions, but she incorrectly equates her own conduct with the vastly different (and much more minor) violations of two other em- ployees—accessing their own standby reservations through the reservation system—who were not fired. Vesey was not fired for merely accessing her own standby reservations

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through the wrong system; she was fired for defrauding her employer. No evidence offered by Vesey creates a genuine dispute that would allow a reasonable jury to conclude that Vesey was terminated for any reason other than her abuse of travel benefits. Vesey also faults the district court for improperly rejecting her hostile work environment claim. She contends the racist actions of Masengarb, combined with the retaliatory actions of White and McMurray—being rude to her, and saying they did not want to work with her and wanted her fired— amounted to a hostile work environment. The district court was still correct to grant Envoy summary judgment on this claim. Envoy avoided any liability for Masengarb’s remark by promptly investigating Vesey’s complaint and terminating him. Montgomery v. Am. Airlines, Inc., 626 F.3d 382, 390 (7th Cir. 2010) (holding that employer liability for coworker harassment requires that the employer be “negligent in dis- covering or remedying harassment”). Vesey’s claim that her general manager told other employees she ought to be fired rests only on hearsay. And as we have said, that a supervisor was “standoffish, unfriendly, and unapproachable [does not] establish[] an objectively hostile work environment.” McKen- zie v. Milwaukee Cnty., 381 F.3d 619, 624–25 (7th Cir. 2004). B Vesey also appeals the district court’s denial of her Rule 59(e) motion to alter or amend the judgment given the previ- ously missing portion of Emerick’s deposition. According to Vesey, the newly discovered portion shows that Emerick filed the complaint against her at the urging of White—who Vesey alleges harbored retaliatory animus against her.

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Relief under Rule 59(e) is an “extraordinary remed[y] re- served for the exceptional case.” Gonzalez-Koeneke v. West, 791 F.3d 801, 807 (7th Cir. 2015). It is granted to correct a manifest error—factual or legal—or to consider newly discovered evi- dence. Cincinnati Life Ins. Co. v. Beyrer, 722 F.3d 939, 954 (7th Cir. 2013). We review its denial for abuse of discretion. Id. at 953. Vesey argues the missing part of the transcript is newly discovered evidence. But newly discovered evidence can be grounds for relief under Rule 59 only if the party exercised due diligence in discovering it and, nevertheless, only discov- ered it post-judgment. Id. at 955. Vesey’s lawyers attended Emerick’s deposition, so they were present during the testimony memorialized in the por- tions of the transcript that became the subject of her Rule 59(e) motion. The evidence was therefore discovered on the day of the deposition. Additionally, while preparing her summary judgment filings, Vesey should have noticed that the tran- script was incomplete, especially if the missing portions, as she now argues, were important enough to change the out- come of the case. We agree with the district court that Vesey’s “lack of diligence does not render this evidence newly discov- ered.” See Egonmwan v. Cook Cty. Sheriff’s Dep’t, 602 F.3d 845, 852 (7th Cir. 2010) (denying a Rule 59(e) motion based on a deposition taken after summary judgment briefs were filed, but that could have been taken earlier, because “Rule 59(e) cannot be used to introduce evidence that could have been presented earlier”). Thus, the district court did not abuse its discretion in denying her Rule 59(e) motion. Even considering Emerick’s entire deposition, Envoy was still entitled to summary judgment. Vesey admits that

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Envoy’s investigators were not motivated by any retaliatory or discriminatory animus, and instead she argues a cat’s paw theory. But as explained above, a cat’s paw theory does not apply because the investigators gathered sufficient justifica- tion, independent of the allegedly biased complaint, to fire Vesey. C Finally, the district court ordered Vesey to pay Envoy’s costs, which she contests. Yet in her principal brief, Vesey of- fers only a conclusory remark on the topic: “The Bill of Costs had numerous entries of exorbitant charges and billing of which the Plaintiff-Appellant should not be held accounta- ble.” App. Br. 12, ECF No. 11. “Undeveloped arguments are waived on appeal.” United States v. Collins, 604 F.3d 481, 487-88 n.2 (7th Cir. 2010). In her reply brief she elaborates slightly, but arguments not made in the principal brief are for- feited. United States v. Foster, 652 F.3d 776, 787 n.5 (7th Cir. 2011) (“The reply brief is not the appropriate vehicle for pre- senting new arguments or legal theories to the court”) (quot- ing United States v. Feinberg, 89 F.3d 333, 341 (7th Cir. 1996)). So we need not reach the merits of this argument. For all these reasons, we AFFIRM the district court’s grant of summary judgment to Envoy, denial of Vesey’s Rule 59(e) motion, and order for costs.