Wells Fargo recently notified checking and savings account customers that, effective Feb. 15, its mandatory arbitration agreement—one of the toughest in banking—will become even more ironclad. Meanwhile, Chase is giving deposit-account customers a chance to opt out of mandatory arbitration within 60 days of opening their account.

The Dodd-Frank Act gave the Consumer Financial Protection Bureau the right to ban or restrict mandatory pre-dispute arbitration clauses between financial service companies and consumers, but only if it does a study and finds that doing so is in the public interest and protects consumers. Alan Kaplinsky, who heads Ballard Spahr’s Consumer Financial Services Group and who pioneered the use of such clauses, says he does not think this will be a priority for the new bureau.

“I think when they try to do their study, people will be surprised to find out that consumers who go through arbitration like it very much and they do quite well,” Mr. Kaplinsky said.