If they have admitted underpayment then you should be due FULL back-payment (with interest?) immediately and not be offered a paltry partial payment! If there had been an OVER-payment they would expect it back in full with interest!!!
Ask them on what basis they’re offering less than the full amount, and that it cannot be because you had to scrimp and save to be able to pay the bills. Your hardship cannot be an excuse.
As @Chris_22081 says - if there had been an overpayment, they’d expect it all back.