Do I need to amend NY state tax return after receiving w2-c, if it does not change amount due/owed?

My employer just sent me corrected w-2. The only change is in local wages (box 18), so it only could possibly affect NYC city tax.

 

However when i started amending return in TurboTax and updated W-2, TT told me my total return does not change at all and whether I am sure I want to submit the amendment.

 

Well now I'm not so sure. So... should I or is it not needed?