WASHINGTON — Trade groups representing many of the nation’s largest retailers expressed frustration after the Supreme Court on January 20 declined to take up their challenge to the Federal Reserve’s hotly debated rules for “swipe fees” assessed on credit card and debit card transactions.

Retailers and other businesses pay the fees to banks and other financial companies each time a customer uses one of the cards to pay for goods or ­services.

The fees represent reimbursement to the financial companies for their costs in offering credit cards and executing electronic debit ­transactions.

Retailers — including the National Retail Federation, the Food Marketing Institute and the National Association of Convenience Stores — argued that the Federal Reserve set the fees too high.

A federal court agreed with the retailers in 2013, saying that the Fed “clearly disregarded Congress’s statutory intent by inappropriately inflating all debit card transaction fees by billions of dollars.”

But a federal appeals court last March overturned the lower court’s ruling, saying the Fed had acted reasonably in setting the average swipe fee at 21 cents per transaction, plus a fraud adjustment.

The Supreme Court let that ruling stand without comment.

Congress in 2010, as part of the Dodd-Frank Wall Street Reform and Consumer Protection Act, directed the Fed to set a cap for swipe fees in order to bring them in line with what it actually costs to process the transactions.

Prior to the Dodd-Frank legislation, the average swipe fee was 44 cents per transaction. The Fed’s initial proposal slashed the fee to around 12 cents. After strenuous objections from the financial services industry, the Fed ended up setting the fees at 21 cents per ­transaction.