The letter only gives dates and no reasons or justification for the repayment
First step, challenge the reasons and justification. Make the b*ggers work for the money.
I continued to be paid for 2 months after I retired until I told them. They then demanded repayment of a sum that I contested and demanded that they prove it. I got about £25 interest while they faffed around.
Eventually, after I demanded a copy of the pay manual the penny dropped at their end and they 'proved' their calculation which previously they had failed to do.