It doesn't change anything if he can't itemize this year. The point is, this $177 does not represent a taxable recovery of an amount previously deducted on the 2017 return, because it represents a recovery or rebate or refund of an amount paid a couple months earlier in 2018.
You deal with 2018 on its own, if you don't deduct any state tax, then you don't deduct the final 2017 payment and you don't have to adjust it.
There is no place to "show your work" for this. Keep records, and if the IRS sends a letter asking if the $177 should have been taxable, you reply as we discussed here.
