Filing a DMCA claim is not what you think it is.
You don’t have to copyright your work in order to own it. If you create a work or service, you are automatically the legal owner/ copyright holder of that work. That’s the law. You would only need a formal copyright if you plan to get money from infringers.
Now, DMCA takedown means I own this product, and I don’t want it to be used here. Or I don’t want it used this way. Or I don’t want it used by the this person. As legal copyright owner of your work, you are allowed to issue this takedown. The person may not take it down. But that’s just an invitation for you to sue them. And you would win. So most people don’t go through that hassle which is why cease and desist/ Takedown notices almost always do the job.
He would only have rights to the work if it was implied/given as agreement in a transaction. That work is part of a monetary agreement. If he gets a refund, he no longer has rights to that work. That’s the law. Thats a fact.
Long story short, know your rights. And issue that takedown claim. Like now. Immediately.