You might need to. Activity in an HSA needs to be reported, and that's what Code W is reporting: contributions to an HSA. You are correct that it might not affect your tax liability, but you should report the activity through the amended Form 8889. When asked the reason for the amend, you will state "Amended Form 8889 because of Corrected W-2" and provide a copy of the amended 8889 and the corrected W2 to the IRS.
You probably will not have to correct the state return, (unless you are in California or New Jersey, states that do not allow a deduction for an HSA contribution).
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