For now, the ability to record a refund in QuickBooks Self-Employed is unavailable yet. However, I've got a workaround you may consider doing. You can create a negative (-) invoice/transaction for the customer and send it to prove that you have refunded the customer.
Since the invoice section in QBSE doesn't affect the income or expenses for Self-assessment, you may need to record in the transaction page that expense of paying your customer back. If in case the bank account has pulled at the expense of refunding your customer, you may then need to categorize the transaction. If you're not sure of what category to use, it would be best to consult an accountant to make sure the accuracy of your books.