The bank accounts of about 7,500 people who buy health insurance through the Massachusetts Health Connector were overcharged because of a technical problem that occurred Thursday night.

Dell, the technology company that handles electronic payment processing, “experienced an issue,’’ according to Connector spokesman Jason Lefferts.

“We are working expediently to remedy the situation for the affected accounts,’’ Lefferts wrote in an e-mail. He said the agency would fully reimburse its customers for any fees that result from overdrafts caused by the overcharging, but could not predict when the problems would be resolved.

The Connector is a state agency serving people who don’t obtain health insurance through their employer. Customers use the Connector’s website to select from a menu of insurance plans, enroll their chosen plan, and pay their monthly premiums.

Payments for July coverage were due Thursday, and many customers have their bills paid through automatic withdrawal from their bank accounts. But the glitch at Dell resulted in more money being withdrawn than was owed.

Peter Lowy, a self-employed marketing consultant in Brookline, discovered the error Friday morning: His monthly premium was withdrawn three times. Lowy said he was astonished that such an error was even possible and called the Connector software “woefully unsophisticated.’’

Lowy said he was able to transfer money to cover other bills, but many other people may suddenly face bouncing checks.

Those affected by the overcharges represent a small portion of the 224,000 Connector members.

“Members whose accounts were overcharged are receiving phone calls and e-mails this afternoon with details, and members who contacted us today will receive a call back with an update,’’ Lefferts said Friday.

Frustrating glitches are nothing new for Connector members. When the federal Affordable Care Act required the agency to update its software in 2013, the result was a nonfunctional website that had to be scrapped.

New software launched in 2014 worked better, but bugs in the payment process sometimes prevented premiums from being transferred to insurers. As a result, many people didn’t get coverage.

The latest version of the Connector software, put in place last year, had functioned more smoothly — until Thursday night.

Felice J. Freyer can be reached at felice.freyer@globe.com. Follow her on Twitter @felicejfreyer.