When the number with code W in box 12 changed, did the amount of Wages in boxes 1, 3, and 5 not change? The employer should have removed the amount with code W in box 12 from your Wages before printing your W-2.
You should contact your employer and confirm that they have the correct number for Wages in boxes 1, 3, and 5. If this needs to be changed also, then you definitely file an amended return.
However, it's possible that the employer printed the correct number for Wages but the incorrect number for the code W amount. If your AGI did not change and your income tax did not change, then don't file the amended return, but keep good records in case the IRS writes you a letter asking about the correct W-2.
