This case arises from the world of auto racing and the sponsorships that go along with it, but it is in the wrong court. Panther Brands is a marketing and brand management company. In 2013, Panther signed a contract with IndyCar, which authorizes the Indy Racing League car series, to purchase various marketing benefits to provide to its team sponsor. The benefits included access to coveted space in the “Fan Village” at IndyCar racing events, an area where sponsors set up displays to attract fans. The Army National Guard (“the Guard”) had been Panther’s team sponsor from 2008 to 2013. After it signed the 2013 contract, Panther learned that[*589] another team, Rahal Letterman Lanigan Racing (“RLL Racing”), intended to provide the Guard with Fan Village space as a sponsorship benefit.

Believing that RLL Racing had conspired with IndyCar and a bid management agency called Docupak to persuade the Guard to sponsor RLL Racing instead of Panther, Panther brought suit in state court against RLL Racing, Docupak, Indy-Car, and active-duty Guard member John Metzler, who acted as the liaison between the Guard and Panther. The defendants removed the case to federal court, where the United States was substituted as a party for Metzler, see 28 U.S.C. § 2679(d); Panther then filed an amended complaint that did not name either Metzler or the United States. The district court dismissed the complaint against RLL Racing, Indy-Car, and Docupak pursuant to Federal Rule of Civil Procedure 12(b)(6), and found the United States’s motion to dismiss for lack of jurisdiction moot. Because the basis for federal jurisdiction disappeared when Panther amended its complaint, we vacate the district court’s decision and remand for dismissal for lack of jurisdiction.

I

The Appellees offer several bases for federal subject-matter jurisdiction over this dispute: removal based on the existence of federal-question jurisdiction, 28 U.S.C. §§ 1331, 1441; federal officer removal, id. § 1442; and the Westfall Act, id. § 2679. None succeeds.

A

A defendant may remove a lawsuit to federal court under 28 U.S.C. § 1441 when there is a claim that “arises under the Constitution, laws, or treaties of the United States.” Id. § 1441(c)(1)(A). The federal question must appear in the well-pleaded complaint; a federal defense will not do. See id. (referring to 28 U.S.C. § 1331); Rivet v. Regions Bank of Louisiana, 522 U.S. 470, 475, 118 S.Ct. 921, 139 L.Ed.2d 912 (1998). Panther’s amended complaint asserts that RLL Racing and Metzler formed an agreement that violated “multiple federal statutes and regulations.” IndyCar regards this as an adequate jurisdictional allegation, but it is not. The fact that federal regulations (such as those affecting the Guard’s contracts) may have some bearing on the case tells us nothing about jurisdiction; the question remains whether the claim is based on state or federal law. See Nuclear Eng’g Co. v. Scott, 660 F.2d 241, 249 (7th Cir. 1981) (finding no federal jurisdiction over claims “predicated upon state law that at most incorporates federal law in certain tangential respects”). Panther’s complaint alleges breach of contract, interference with contract, unjust enrichment and conversion, and unfair competition and bid rigging. These are all state-law theories, and none is “essentially federal in character.” Id. Jurisdiction under sections 1331 and 1441 is therefore lacking.

B

The Appellees also invoke 28 U.S.C. § 1442, the federal officer statute, as a basis for subject-matter jurisdiction. Section 1442 permits removal to federal court of an action against “[t]he United States or any agency thereof or any officer (or any person acting under that officer) of the United States or of any agency thereof, in an official or individual capacity, for or relating to any act under color of such office[.]” 28 U.S.C. § 1442(a)(1). Federal-officer removal is possible when (1) the defendant is a “person” within the meaning of the statute, (2) the defendant is “actfing] under” some entity of the United States, (3) the defendant is acting under color of federal authority, and (4) the de[*590] fendant has a colorable federal defense. Ruppel v. CBS Corp., 701 F.3d 1176, 1180-81 (7th Cir. 2012).

IndyCar and the other appellees contend that Docupak acted as a federal officer and thus that this was a valid basis for their removal. We accept that Docupak is a “person” within the meaning of section 1442, according to the law of this Circuit. 'Id. at 1181; contra Roche v. Am. Red Cross, 680 F.Supp. 449, 455 (D. Mass. 1988) (concluding that “the text of section 1442 suggests that only natural persons are covered”). But we run into trouble when we consider whether Docupak was acting for a governmental entity and under color of federal authority.

Docupak says that it “acted under” the Guard by collecting and summarizing bids for the Guard’s sponsorship. There are indeed cases supporting this form of removal “where the federal government uses a private corporation to achieve an end it would have otherwise used its own agents to complete.” Id. The Supreme Court applied this doctrine in decisions finding persons to be acting under federal entities when assisting in distillery raids during Prohibition. Maryland v. Soper, 270 U.S. 9, 30, 46 S.Ct. 185, 70 L.Ed. 449 (1926); Davis v. State of S. Carolina, 107 U.S. 597, 600, 2 S.Ct. 636, 27 L.Ed. 574 (1883); Tennessee v. Davis, 100 U.S. 257, 261, 25 L.Ed. 648 (1879). Other courts have held that private entities were acting under the federal government or its agencies for federal-officer removal purposes when providing benefits to federal employees under the direction of the Office of Personnel Management, Jacks v. Meridian Res. Co., LLC, 701 F.3d 1224, 1234 (8th Cir. 2012); when manufacturing Agent Orange for the United States, Winters v. Diamond Shamrock Chem. Co., 149 F.3d 387, 399-400 (5th Cir. 1998); and when operating environmental preserves pursuant to National Oceanic and Atmospheric Administration grants, Town of Davis v. W. Virginia Power & Transmission Co., 647 F.Supp.2d 622, 630 (N.D. W. Va. 2007).

We grant that private contractors performing tasks for the government are sometimes covered under section 1442, but Appellees take this idea too far. We held in Lu Junhong v. Boeing Co., 792 F.3d 805, 810 (7th Cir. 2015), that merely being subject to federal regulations or performing some functions that the government agency controls is not enough to transform a private entity into a federal officer. Indeed, in Watson v. Philip Morris Cos., Inc., 551 U.S. 142, 127 S.Ct. 2301, 168 L.Ed.2d 42 (2007), the Supreme Court held that “the fact that a federal regulatory agency directs, supervises, and monitors a company’s activities in considerable detail” does not suffice to make that company a “person acting under” a federal officer. Id. at 145, 127 S.Ct. 2301. Docupak’s activities on behalf of the Guard fell far short of the closely monitored and highly regulated relationships involved in the distillery, federal benefits, Agent Orange, or oceanic preserves eases on which it relies. Neither did the Guard delegate any rulemaking authority to Docupak, which we have suggested might make a difference. See Lu Junhong, 792 F.3d at 810. Jurisdiction under the federal-officer removal statute was thus also unavailable.

C

Finally, IndyCar argues that the Westfall Act, 28 U.S.C. § 2679, furnishes jurisdiction for its case. That statute immunizes federal employees acting within the scope of their employment from an action for damages through the device of substituting the United States as the party defendant, so long as the suit is not for a constitutional violation or otherwise statutorily authorized against a government[*591] employee. 28 U.S.C. § 2679(b)(2), (d). Once the Attorney General certifies that the named employee was acting within the scope of his office or employment, federal jurisdiction becomes exclusive. See Osborn v. Haley, 549 U.S. 225, 242, 243, 127 S.Ct. 881, 166 L.Ed.2d 819 (2007) (“For purposes of establishing a forum to adjudicate the case, however, § 2679(d)(2) renders the Attorney General’s certification dispos-itive ... Congress has barred a district court from passing the case back to the state court where it originated based on the court’s disagreement with the Attorney General’s scope-of-employment determination.”). If after full consideration, the district court determines that a Westfall defendant committed tortious conduct outside the scope of his federal employment, the court may retain jurisdiction, because a significant federal question — whether the employee had Westfall Act immunity— would have been present in the case from the outset. Id. at 244-45, 127 S.Ct. 881.

The case before us does not fit that pattern. After the United States (standing in for Metzler) was eliminated as a party as a result of Panther’s amendment of the complaint, the basis for federal jurisdiction disappeared. This is so even accepting that Westfall Act removal was appropriate initially.

II

Because we find the district court had no jurisdiction over this dispute, we vaoate the district court’s judgment and remand for dismissal op that basis.