According to the State of Missouri on their website, anytime an employee is performing work for a Missouri employer, the wages earned are subject to Missouri withholding. So you will need to file a Missouri non-resident return to get that money back. Also if your wages are more than $600, you will need to file a MO non-resident return regardless if taxes were withheld or not.
The good news is this MO link states that if a nonresident employee performs all of his or her services outside of Missouri, the wages paid to that employee are not subject to Missouri withholding. Please view this Missouri link for further details.
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