Shipping the wrong product to the customer is bad customer service, fact. It always leaves a bad impression regardless of the good will of the customer. And no matter the circumstances, it is always you who are the guilty party.
This is one of the most unfortunate aspects of drop shipping. No matter what the mistake and who made it, it is always you and your reputation that suffers.
Best Way to Handle:
First of all, know your producer or drop shipper’s return policies back to back. In fact, you should know them before you ship your first product. This way, when the complaint from a customer comes, you will be able to instruct them on what to do straight away.
Also, it is a good idea to offer a customer a discount for a future purchase or at least a small token to apologize for your mistake.