It is paid back through your federal tax return.
The form with the return is 8962.
I found this information on the IRS website: https://www.irs.gov/affordable-care-act/individuals-and-families/questions-and-answers-on-the-premiu...
23. Will I have to file a federal income tax return to get the premium tax credit?
Yes. For any tax year, if you have APTC in any amount or you do not have APTC but you plan to claim the premium tax credit, you must file a Form 8962, and attach it to your federal income tax return for that year. If you have any APTC, you will use Form 8962 to reconcile the difference between the APTC made on your behalf and the actual amount of the credit that you may claim on your return. This filing requirement applies whether or not you would otherwise be required to file a return.
25. How do I reconcile APTC with the actual premium tax credit on my return?
When you complete your tax return, you will figure your credit and compare it to the amount of APTC on Form 8962. If your actual allowable credit on your return is less than your APTC , the difference, subject to certain repayment caps, will be subtracted from your refund or added to your balance due. If your actual allowable credit is more than your APTC , the difference will be added to your refund or subtracted from your balance due. (See question 4 for information on changes in circumstances.
26. What are the repayment caps?
The repayment caps limit how much of the excess APTC you must repay and are based on your household income and filing status. If your household income reported on your tax return is 400 percent of the FPL (which is based on household income and family size) or higher, you must repay the full amount of APTC that exceeds your premium tax credit. See Publication 974 for more information on the repayment caps.