The American Express Co. saleswoman had finally convinced Bryan Daughtry to apply for a card. There was just one thing: She had to run a credit check.

Mr. Daughtry, who owns a disaster-cleanup company in Ohio, balked. He was trying to get a mortgage and didn’t want the inquiry to dent his credit score. She refused to stop the process, he said, checked his credit, and his application was approved.

“That left a bad taste in my mouth,” said Mr. Daughtry.

Some AmEx salespeople strong-armed business owners like Mr. Daughtry to increase card sign-ups, according to more than a dozen current and former AmEx sales, customer-service and compliance employees. The salespeople have misrepresented card rewards and fees, checked credit reports without consent and, in some cases, issued cards that weren’t sought, the current and former employees said.

An AmEx spokesman said the company found a very small number of cases “inconsistent with our sales policies.” “All of those instances were promptly and appropriately addressed with our customers, as necessary, and with our employees, including through disciplinary action,” he said.