1. If you paid IL income tax on 100% of your income (including your earnings from WI), and you did NOT take any Other State Credit on your IL return, then there is no need to amend your IL return.
2. You should respond to the letter from WI by explaining that you are a full-year resident of Illinois and thus you do not owe WI taxes on your W-2 income. This may result in WI correcting the situation without your needing to file a WI tax return.
3. If your WI employer is still withholding WI taxes, you should do as @Anonymous stated and file WI Form W-220 with your WI employer. Here's a link to that form:
https://www.revenue.wi.gov/TaxForms2017through2019/w-220.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
