First of all, an F1 visa holder is only exempt from Medicare and Social Security tax while they are working within the scope of their educational visa. They are not exempt from those taxes if they take a job that is outside the scope of their visa.
Assuming that you are correct, and that your wife will eventually receive a refund of the incorrectly withheld Social Security and Medicare tax and will receive a corrected W-2 showing zeros in box 3, 4, 5, and 6, that will not affect your federal tax return. The federal tax return is based on box 1 taxable wages, and as long as the box 1 taxable wages don’t change, nothing else that might change will change the federal tax return or require an amended return.
however, if she is an F1 visa holder who has been in the country less than five years and is exempt from Social Security and Medicare tax, then she is also considered a non-resident for income tax purposes and cannot file a joint return with you—unless you make an election to treat her as a US resident for income tax purposes. You may have made this election already, but if not, you may want more information for your situation.
