You don't do anything on your 2018 tax return. That is, you pay full tax on your 2018 W-2 amount, unless they issue you a corrected W-2 (unlikely).
If the Military shows the repayment as a reduction of income on your 2019 W-2 (likely), all you will have to do is report your W-2 normally. If not see below for how you will handle your 2019 tax return (when you file in 2020).
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Repayments. This situation is described in IRS Publication 525. pgs
34-35. If the amount is more than $3000,
you can take a itemized deduction, on
line 16 of schedule A or you can take a credit. The credit is computed
by refiguring the tax return 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. In the forms mode (the
forms mode is not available in the on-line versions of TurboTax[TT]), you can
use the line 74 smart work sheet to enter the credit amount on line 74; select
item D, claim of right under IRC 1341 for repayments. TT will enter "I.R.C.1341" on the line next
to box d on line 74 of form 1040 (schedule 5). TT does not do the credit calculation
or compare it to the alternate deduction.
So, the taxpayer has the option of
either claiming the credit or deducting the repayment as a miscellaneous itemized
deduction, whichever provides the greater benefit. But, you cannot file an
amended prior year return.
If the amount is $3,000 or less, no deduction or credit is allowed. In the
past, a miscellaneous itemized deduction, subject to the 2% of AGI threshold,
was allowed. But, all miscellaneous
itemized deduction, subject to the 2% of AGI rule go away in 2018. I've seen
nothing yet to indicate if there will be an exception for repayments of income
