Wise has been accused by a rival fintech company of undermining competition in the money transfer market.

Atlantic Money, a smaller foreign exchange service, made this allegation in a letter to the U.K. competition watchdog, the Competition and Markets Authority.

Shares of Wise, which debuted on the London Stock Exchange in 2021, were worth £5.14 apiece at 10:30 a.m. London time, 2% below the Thursday market close.

Wise has a market capitalization of £5.3 billion ($6.6 billion).

In the letter Atlantic Money shared with CNBC, the company says Wise unfairly removed it from the price comparison section of its website and refused to include it on Exiap — a foreign exchange fee comparison site that also belongs to Wise.

Wise owns two other currency transfer comparison sites, Geldtransfer and Currencyshop.

Atlantic Money said in the letter that it was initially listed by Wise on its website on Oct. 14, 2022. It was later delisted on Jan. 20, 2023, with Wise allegedly telling Atlantic Money it was "no longer deemed a legitimate competitor."

In the letter, Atlantic Money said it believed Wise's conduct was "harmful to competition across the UK and EU and, we would submit, ultimately results in higher fees for end consumers."

Atlantic Money offers a flat £3 fee on all currency conversions up to £1 million. Its fees are lower than Wise for transfers of £1,000 or more.

Formerly known as TransferWise, Wise has long touted itself as a champion of consumer rights, pushing for transparency around the fees charged by banks to move money across borders.

"We decided to remove Atlantic Money for the time being for a number of operational reasons, including queries received from customers about their business. We take any complaints very seriously," a Wise spokesperson told CNBC via email, in response to a request for comment on the Atlantic Money letter.

"We're really proud to have the comparison tool as part of our website, and we're not afraid to list cheaper competitors. We've done that for years and still do."

The letter could be a precursor to a probe investigating whether Wise's conduct breaches competition law.

A CMA spokesperson said that the regulator was unable to comment on specific cases outside of a formal investigation.