You can file a nonresident return for the incorrect state to get the withholding back. Indicate in that return that you don't have income sourced in that state if that's the case.
Prepare the nonresident state return first, then your resident state return. If you did end up with any tax liability paid for the nonresident state (not the withholding, but any actual tax shown in the state return), you may be able to take a credit for it on your resident state return.
See also this TurboTax article on multiple-state situations.
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