If customer inquiries are handled by Suppliers, the Supplier should process the refund in Shopify. The refund will flow from Supplier to Storefront to customer.
If customer inquiries are handled by the Storefront, the Storefront can choose to process the refund in Shopify, if the Storefront is hosted on Shopify. Refunds will flow from the Storefront to the customer. The Storefront then must separately request a refund from the Supplier. If the Storefront is using Canal's API, then it will need to create a refund request using the /refunds/ endpoint.