Yes, I still have the receipt. Is the best approach to write a letter to them with a photocopy of the receipt?

Hi, 1st post so please take it easy on me!! I stayed at a leisure resort in January and on leaving, paid the full bill amount as stated by the receptionist. The receipt clearly states full balance paid. About a week ago, I received an invoice from the leisure resort basically stating the had miscalculated the amount and I was due them more money. Am I liable to pay this money given that my receipt states I have paid the full amount and the mistake was made at their end? Thanks.