If you did not live in or have any income from IL during the year, you owe no IL taxes, so no IL taxes should have been withheld from your check.
Unfortunately, you'll have to file a non-resident IL return, showing zero IL income, in order to get a refund of the incorrectly withheld IL taxes.
Of course you should also inform your payroll department that you are an MO resident working only in MO, so that they cease withholding IL taxes.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
