Hello, @MarC168 !
Karlie here from the Shopify Guru Team! Can you let me know what payment gateway the merchant had used for payment processing when they had put through their order? You can find this information out by checking the timeline of the order. If it was Shopify Payments and it shows that the refund went through successfully on the order page of your Shopify Admin, then you would want to have the customer reach out to the bank or credit card company to inquire. If you're using a third party payment gateway, you can always reach out to their support team to see if there were any issues when refunding the customer.
Looking forward to hearing back from you!