Illinois and Wisconsin have reciprocity which means you only pay income taxes in your resident state on wages earned in WI. you should have filed a WI return reporting none of your WI wages as taxable so you would get back WI withholding. if you didn't you need to file an amended WI to get it back.
Submit exemption Form W-220 to your employer if you work in Wisconsin and are a resident of Illinois. This will stop WI w/h.
note: you also must make sure that your employer withholds IL taxes. if they won't you need to pay IL estimated taxes to avoid penalties for underpaying your taxes.
you can file a claim against Turbotax for the penalties and interest. however, if the error was due to a mistake on your part rather than a programming error the claim will be denied
https://ttlc.intuit.com/community/choosing-a-product/help/what-documents-do-i-need-to-submit-a-claim...
