Citigroup Inc. and a big hedge-fund client are locked in an uncharacteristically public feud that has embroiled top executives at both firms and laid bare a $900 million mistaken payment by the bank.

At the root of the dispute: Citi’s role helping billionaire investor Ron Perelman restructure the corporate loans of cosmetics company Revlon Inc. Some investors wanted Citi to bow out of the transaction; when it didn’t, they blamed the bank for facilitating a deal that hurt their investments, according to people familiar with…