@taxes_due What @AmyC states on her response is absolutely correct for 2021. Indiana reconciles county tax as part of the state return, and because local tax it is not part of the reciprocal agreement with Kentucky, they do provide a credit for out-of-state local taxes paid, limited up to the amount of local tax you would pay based on the county where you live. As @KrisD15 mentions, this is separate from the state reciprocal agreement.
So for 2021, not reporting the taxes you paid to Louisville (I know it's Louisville by the form you mention) is the best way to set things straight with Indiana to determine your county tax if you are counting on having all of the Louisville local tax withheld refunded to you. Everything will calculate correctly for you.
For 2020, you will need to file an amended return with Indiana to release the credit you claimed for local taxes paid to another state on Schedule 6. If Louisville tax withheld was greater than your county tax rate, then you are correct that you will not have to pay the entire refund back. Also, if you had to pay a second local tax (Shively, Jeffersontown, or St. Matthews, for example), you can claim those taxes paid towards a credit of Indiana local taxes if you did not receive a refund for those taxes. If applicable, this will lower what you will pay back to Indiana.
This Help Article will provide assistance on how to prepare the amended state return: I need to amend my state return
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