You do not get a direct refund of the federal income tax that you paid. Since the amount you repaid was more than $3,000 you can get a deduction or a credit on your 2022 tax return. The two options were explained to you when you asked about it in March and again earlier this month, at the following links.
Paying back relocation tax refund
Returning gross relocation payment tax refund
You are correct that FICA is the Social Security and Medicare taxes. Regarding those taxes, IRS Publication 525 says the following.
"Repaid wages subject to social security and Medicare taxes. 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."
You cannot use TurboTax to file Form 843.
Please do not post any more separate questions about your repayment. It's too confusing and hard to follow, and hard to see the whole picture, when information about one issue is scattered in multiple threads. If you have further questions about the repayment, add a reply to this thread.
