The correction to the W-2 could change a little or a lot on your return, and you won't know which until you go through the amendment process in TurboTax. The change could create or eliminate an excess contribution in TurboTax.
Also, the employer should have removed the box 12 code W amount from your Wages in boxes 1, 3, and 5 on your original W-2. Did they remove the correct amount the first time? Did they change Wages on the corrected W-2? If yes to changing Wages, you definitely need to file an amended federal and state return. You must ask your employer if they have taken the correct amount out of Wages, in case they made two mistakes instead of one.
The code W amount appears on your 8889, but might not have any effect on the rest of the return. In this case, if you choose not to amend because your AGI and tax due don't change, you need to keep good records, in case the IRS notices some discrepancies and writes you a letter for an explanation.
If, however, your state return is from one of three states (California, Alabama, and New Jersey), then you must file an amended state return (which will require you to amend the federal anyway), because HSA contributions are not deductible in these states, and the amount of the contributions (i.e., the code W amount) is added back to state income.
