Ms. Zeleny, a lawyer who lives outside Salt Lake City and opened a Wells Fargo account when she started a new law practice, said it would be impossible for her to agree to arbitrate her dispute over an account that she had never signed up for in the first place.

The bank’s counterargument: The arbitration clauses included in the legitimate contracts customers signed to open bank accounts also cover disputes related to the false ones set up in their names.

Some judges have agreed with this argument, but some lawmakers and others consider it outrageous.

“Wells Fargo’s customers never intended to sign away their right to fight back against fraud and deceit,” said Senator Sherrod Brown, an Ohio Democrat, who introduced a bill last week that would prevent Wells from forcing arbitration in the sham account cases.

Yet even as the bank reels in the court of public opinion, Wells Fargo has been winning its legal battles to kill off lawsuits. Judges have ruled that Wells Fargo customers must go to arbitration over the fraudulent accounts.

In dismissing one large case seeking class-action status in California, a federal judge ruled last year that it was not “wholly groundless” that customers could be forced to arbitrate over accounts they had never agreed to. That case is now being settled, according to legal filings.

In a statement, Wells Fargo said it was working with customers to reimburse any improper fees. If the issues are still not resolved, the bank offers free mediation services. Arbitration, the bank said, is a “last resort.”

“We want to make sure that no Wells Fargo customer loses a single penny because of these issues,” the statement said.