Strictly speaking, if your brother cancelled the membership (and therefore the direct debit), the gym should not have collected any futher premiums.
The Irish Payment Services Organisation (IPSO) manage the Direct Debit Scheme and according to :
In this case your brother is the payer and his bank is the Originator. Not so - the Gym are the originators
However, as others have said, if your brother cancelled his membership before the contract expired, then the gym are legally entitled to the balance due, even if technically they shouldn't have collected it via direct debit. In the gym's defence though, and speaking generally, if they instead sent an invoice for any balance, they run the risk of getting nothing back.
If it is a case that the contract has expired, or it was a month to month membership, then they are obliged to refund the money. The first port of call would be a registered letter to the bank, copied to the gym manger, stating that direct debits were paid after a DD was cancelled and that a refund is required. Give as much detail in the letter as possible: the dates and amounts of the collections, when the cancellation letter was sent and who it was sent to.