Under the Affordable Care Act, people who remained uninsured last year must either pay a penalty with their taxes, one of the most contentious elements of the law, or claim an exemption. The Obama administration has said up to six million people would owe a penalty of $95 or 1 percent of their household income, whichever is greater. But as many as 30 million people are getting exemptions, mainly because they are too poor to afford health insurance or because they live in a state that refused to expand Medicaid last year under the health law.

And people who did get insurance but, like Mr. Ciesielski, underestimated their income for 2014 — the figure on which subsidies are calculated — are being required to pay back part of their subsidy.

In late February, H & R Block reported that its uninsured clients had paid an average penalty of $172. The money comes out of refunds, while people who do not get refunds are required to pay the Internal Revenue Service by April 15.

The health law prohibits the I.R.S. from imposing criminal fines or putting liens on the property of people who ignore the insurance mandate, but it does allow the agency to collect the penalty by reducing future refunds.

“It will still be on their books,” said Courtenay Murphy, a tax preparer in Gunnison, Colo.

H & R Block also found that as of Feb. 24, just over half of its clients with subsidized marketplace coverage had to repay a portion of their subsidy because their 2014 income turned out to be higher than what they estimated when they applied for coverage.