Zions did not interact directly with the company that called Mr. Koch, National Health Net Online. What the bank did was establish a banking relationship with an intermediary, Modern Payments, that handled payments for National Health. Mr. Koch’s account at a small Virginia bank was debited by National Health, which in turn paid Modern Payments for processing the transaction. Modern Payments gave its bank, Zions, a cut of its fee.

In all, Zions in effect let roughly $39 million be withdrawn from hundreds of thousands of accounts from 2007 to 2009. Much of that money was ultimately transferred to bank accounts in Canada, India and the Caribbean, according to a Times review of court records. Many of the Internet merchants’ customers were older people and others on shaky financial footing. But that, too, worked in banks’ favor: the withdrawals set off a cascade of insufficient fund fees — more than $20 million in all, court records show.

“Zions takes seriously the need to prevent the banking system being used for fraudulent purposes; however, it is our general policy not to comment on pending legal matters,” said James R. Abbott, director of investor relations for Zions. “There is another side to this story, other than that told by the plaintiff. Our side of the story will be told at the appropriate time through the legal system.”

A spokesman for First Delaware declined to comment. Neither National Health Net Online nor Modern Payments responded to e-mails and telephone messages.

Mr. Koch, a retired teacher, said that he was usually skeptical of telemarketers. But when his phone rang one afternoon in November 2007, he recalled, he listened as the caller identified himself as a Medicare official and suggested that Mr. Koch update his health insurance card. Mr. Koch, as requested, supplied his bank information.

But instead of a new insurance card he received notice that he had been enrolled in National Health Net Online’s discount health plan. The company had withdrawn $299.95 from his bank account as payment, according to records reviewed by The Times.

National Health, a unit of NHS Systems Inc. of Collegeville, Pa., has a troubled history. In April, the Federal Trade Commission permanently banned the company from telemarketing and ordered it to pay a $6.9 million fine after accusing NHS Systems of defrauding consumers. NHS Systems did not return multiple telephone calls seeking comment.