How do I recoup taxes taken out of a bonus that was paid to me in a combat zone?

You just have to submit proof to your finance that you were in a CZTE designated area during your reenlistment. Your TCS orders will suffice. DFAS is the one who withholds the taxed amount, so that's who you have to recover it from.

You can make an amendment on your tax return. I would suggest going to a tax professional after you visit your reenlistment NCOIC and Finance office at your local soldier support center.

You will have to probably speak with the IRS and your state for your home or record and prove you were deployed to a combat zone and then they would have to make tax adjustments to you.

Your taxable income will remain the same for tax year 2020, despite the bonus. When you file your tax return next year, you will still have the same tax liability as if you had never received the bonus, but you will have significantly overpaid. You should get it all back when you file your return in addition to any other overpayment, which should also be substantial since the deployed time and standard deduction will likely put you in the lowest tax bracket. This will be one hell of a refund. It’ll be like getting another bonus next February.

The only way to get back the federal (and state if withheld) taxes is to remove that amount of income from your tax return. If the amount is included in Box 1 of your W2 then you will need to remove it, possibly on Line 8. If it does not show in Box 1 but the tax withheld shows in Box 2 then you don’t need to do anything, it will work itself out on your return.