At the beginning on 2024, I had to pay back a portion of tuition reimbursement received from my employer in 2023. Is there a place to report/claim that loss?

The first $5250 of tuition reimbursement is tax free.  If you paid back that amount, or less,  there would be nothing for your to claim. on your tax return. 

If the amount was more, the amount over $5250 would have been included on your W-2 and you paid tax on that part. There may be some tax relief, depending on the amount. 

This situation is described in IRS Publication 525.  If the amount is more than $3000, you can take a itemized deduction, on line 16  of schedule A (not subject to the old 2% of AGI rule) or  you can take a credit. The credit is computed by re-figuring the tax from the previous year as if the income had not been received. Then the difference in tax is claimed as a credit on the current year's return.  TT does not do the credit calculation or compare it to the alternate deduction. You have to do that manually. You enter the credit in the forms mode (the forms mode is not available in the on-line versions of TurboTax [TT]). All entries that seem like you should be able to enter on Form 1040 or Schedules 1 through 3 have to be entered on TurboTax's 1040 Worksheet. Scroll way down to Other Credits and Payments Smart Worksheet. Select item E, claim of right under IRC 1341 for repayments. It ends up on line 13b of schedule 3 (2024).

So, the taxpayer  has the option of either claiming the credit or deducting the repayment as an other itemized deduction, whichever provides the greater benefit.  But, you cannot file an amended prior year return.  If the amount is less than $3000, there is no tax relief available.

TT support article.  https://ttlc.intuit.com/community/unemployment-taxes/help/what-is-a-claim-of-right-repayment/00/2153043