It is possible to get some or all of it back.
You would, however, have to file a non-resident WI return.
The below is from the WI DOR web site.
"Even if you do not have to file, if you had Wisconsin income tax withheld from your wages or you paid estimated tax, you should file a Wisconsin return since this is the only way to get a refund."
Source: under #1, https://www.revenue.wi.gov/Pages/FAQS/pcs-npr.aspx#npr1
With your current program, you could add the State of WI to it.
If your WI gross income is below $2,000 no return is required unless you are filing to get a refund.
