Got Let go from a job, collected unempl for 4 months, now they want to appeal it?

First I live in Michigan. I was quote "let go" from a position. It was a doctors office where we check patients insurances each day for the following day to make the work-flow a bit lighter for whoever is on front desk the next day. There are 4 people who regularly rotate the front desk, myself being one of them. Rules are if you get a phone call for a new patient, even exhisting ones, you verify their insurance numbers the day before they come in.The doctor who is also the owner, held a meeting and stated that if it takes too long to verify the patients insurance, that we are to just stop them at the desk, get their card numbers, verify it and if we are unable to then they pay cash. On a day I was off another front desk employee pulled charts, did not verify them. The next day myself and one of the other front desk people attempted verification and were able to verify all but 6 of the stack of 40 of them. I was let go, nobody else, the following Monday. The manager, who is also the doctors wife said I didnt do my duties, when clearly myself and another tried. She also told me that I am a wonderful person, and would give me a recommendation should I need one by phone to any future employers. That I just wasnt working out for them. She stated the Doctor did not want me to gom but that she felt it had to be done. She even asked if I could stay at least till the lunch break to leave. Which I did, no problem. I liked it there. When lunch time came, I gathered my stuff, said my good-byes, to which she had a piece of paper for me to sign. Just said "release of duties" at the top. I signed it because I was afraid that if I didnt then she would no longer give a positive referal to a future employer. I filed unemployment and got approved, however now after 4 months they are just now appealing it. I received a letter stating possible overpayment and I have to fill out the form. What can I do? I did my job to the best of my abilities and have the other young lady that worked with me that day on the patients insurance willing to also write a letter on my behalf. Thank you for looking.