LCS: Still accepted money for a closed account.

Lynneypinney01

I been paying LCS a monthly fee to repay an overpayment on tax Credits since August 2011.
Yesterday I mistakenly sent them an overpayment.  I contacted LCS to ask for advice and if I could request a refund.  They informed me that my account had been closed on 23th June 2023 as the amount owed had been paid in full.  I never received any comms to tell it had been repaid or have they sent a letter to ask me to stop making payments.
They informed me that the money I have paid since June 2023 has been passed to HMRC and I need to ask them for a refund.  I really don't understand why they haven't been in touch and I am not sure how I will get this amount back as LCS are saying HMRC have the money.  Has anyone else experienced a similar issue and what advice can you give.  I am tempted to raise a complaint with LCS on the basis they should have contacted me to stop making payments.