How to claim repayment to 3rd party insurance?

Are you referring to medical insurance reimbursements? If so, IRS Publication 502, page 17, states:

How Do You Treat Reimbursements?

You can include in medical expenses only those amounts paid during the tax year for which you received no insurance or other reimbursement.

Insurance Reimbursement

You must reduce your total medical expenses for the year by all reimbursements for medical expenses that you receive from insurance or other sources during the year. This includes payments from Medicare.  Even if a policy provides reimbursement only for certain specific medical expenses, you must use amounts you receive from that policy to reduce your total medical expenses, including those it doesn't reimburse.

Or are you referring to the repayment of taxable income?  

If you received taxable income in 2022 and paid all or a portion back in 2023, you qualify for a claim of right repayment.

A claim of right repayment occurs when a taxpayer is required to repay income that they had reported and paid tax on in a previous tax year. The repayment must be of funds that, when received, the taxpayer had a reasonable belief he or she had unrestricted access to.

There are two options.  One is for an amount repaid of $3,000 or less.  The second is for an amount repaid of more than $3,000.  For either option, follow these steps.

• Down the left side of the screen, select Federal.
• Down the left side of the screen, select Deductions & Credits.
• Scroll down to Other Deductions and Credits, and click the down arrow to the right.
• Click Start / Revisit to the right of  Other Deductible Expenses.