Overpayment letter from the unemployment office - 6 months and counting

I received a letter saying I was overpaid about $600 on my claim. This is my first time dealing with any of this. The letter mentions an appeal window and a repayment plan. Has anyone disputed one of these?

Collect your pay stubs and certification records for the weeks they name. Mine showed the error was a date mix-up.

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.