The Consumer Financial Protection Bureau on Thursday proposed reversing a ban on exorbitant credit card sign-up fees, frustrating consumer groups and raising questions about the scope of the agency’s authority.

At issue are “fee-harvester cards” that are targeted at consumers with poor credit histories. The cards typically come with low limits, high fees and interest rates of up to 36 percent.

Congress tried to rein in those costs three years ago as part of its sweeping retooling of the credit card industry by capping the fees an issuer can charge at 25 percent of the card’s limit during its first year of use. For example, a card offered by First Premier bank with a $300 credit limit comes with a $75 annual fee — within the boundary set by Congress.

But the card also comes with a $95 processing fee that avoids the law by requiring consumers to pay it up front, before opening the account. In 2010, the Federal Reserve tried to extend the cap to include those charges. First Premier sued, saying the Fed overstepped its authority. In September, the U.S. District Court in South Dakota granted First Premier a preliminary injunction that prevented the rule from taking effect while the legal challenge continued.

“This fundamental shift in statutory policy goes against a clear mandate by Congress and is arbitrary, capricious, and contrary to the Board’s statutory authority,” U.S. District Judge Karen Schreier wrote.

The CFPB took over responsibility for consumer regulations from the Fed and other agencies when it was launched in the summer. Thursday’s proposal essentially undoes the Fed’s regulation and would allow First Premier to impose a sign-up fee.

Miles Beacom, chief executive of First Premier Bank, said the firm’s attorneys are reviewing the proposal. The bank’s lawsuit is ongoing.

“We’re hopeful that it is written so that we’ll be able to continue to market and price the product for the risk and that the customers make a decision whether they want the product or not,” Beacom said.

But consumer advocates expressed dismay that the agency seemed to be shrinking from a legal battle. More broadly, they said the agency should vigorously defend its authority to write strong regulations.

“I was a little bit disappointed in it, and that’s why we’re pushing back,” said Ed Mierzwinski, consumer program director at U.S. PIRG. “The way to protect consumers is to push back when courts make mistakes.”