A customer returned a product that's not on their return request?

Resolve the common issue of product mismatches in return requests with our guidance. Rectify incorrect return information, ensure accurate customer credit.
It really depends on the circumstances. Is this an edge-case or does this happen often?
If this is an edge case, it is easier to just process the returned items. One thing to keep in mind is that customers might file a chargeback if they sent items and didn't receive a refund. In this case, e.g. PayPal would side with the customer because the merchant got the product back.
If this happens frequently, it would be best to improve the client-merchant communication upfront. You can do this by explaining this to your customers through the Approved Email Template and on your returns policy page. If customers know the consequences beforehand, this would greatly reduce the number of identical cases.