The relocation assistance repayment will be reported as a claim of right repayment. It is reported on the tax return for the year in which the repayment was actually made. Therefore, if you pay back the full $9,750 sometime this year, you can report it on your 2024 tax return, which is filed in 2025.
You have the choice of taking a simple deduction or taking a refundable credit of the amount of income tax you previously paid on that income. You can calculate the amounts both ways and determine which is more beneficial to you financially. Instructions on both methods can be found here.
In your question, you stated that you will not be able to repay the relocation assistance right away. If you are able to agree to some sort of payment arrangement, please keep in mind that there is no tax benefit if you repay less than $3,000 per year. Per the IRS, the total amount repaid is calculated per calendar year and is not considered separately.
Lastly, since you are paying back the gross amount of the relocation assistance, you are also repaying the Social Security and Medicare taxes. Publication 525 (page 38) states that if you had to repay an amount that you included in your wages or compensation in an earlier year on which social security, Medicare, or tier 1 RRTA taxes were paid, ask your employer to refund the excess amount to you. If the employer refuses to refund the taxes, ask for a statement indicating the amount of the overcollection to support your claim. File a claim for refund using Form 843.
If you are unable to get that statement from the previous employer, then you can attach a statement with similar information. Full IRS instructions can be found here.
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