WASHINGTON – Reebok agreed Wednesday to refund $25 million to customers who bought its popular EasyTone and RunTone shoes as part of a settlement with the Federal Trade Commission, which says the company did not have the science to back its “better way to a better butt” claims.

The settlement, which must be approved in court, prohibits Reebok from making further unsubstantiated claims regarding the strengthening and toning benefits of the shoes. Reebok started making the pitch in print, television and Internet advertisements in 2009, but pulled the ads in the midst of the FTC probe.

“Advertisers can’t make claims about their product without having some basis for it,” said David Vladeck, director of the FTC’s Consumer Protection Bureau. “That’s the law.”

Reebok issued a statement Wednesday defending its toning shoes, which it said have received “overwhelmingly enthusiastic feedback” from thousands of customers.

“In order to avoid a protracted legal battle, Reebok has chosen to settle with the FTC,” the company’s statement said. “Settling does not mean we agreed with the FTC’s allegations; we do not.”

The EasyTone and RunTone shoes sell for $80 to $100. It’s unclear whether consumers who bought these shoes, as well as Reebok’s JumpTone and TrainTone footwear, will get a full refund.

The FTC first must determine how many customers want their money back. At that point, the agency will be in a better position to divvy up the money among consumers. To request a refund, go to Ftc.gov/reebok.