A refund is generally not provided by most injectors as there is a substantial cost to the filler itself and unfortunately no 100% guarantees. That said, choosing the right patient for tear trough filler is critical, and some physicians will offer other services to make up for the insufficient outcome so as not to lose the patient.
In almost all cases, a refund is not given because yes, you paid for the procedure and doctor, elected to do something that has varying outcomes, and used a product that the doctor cannot get back out of your face. Now, applying it toward another procedure, maybe. But a straight out refund, I don't see happening on very many occasions. It's unfortunate I understand, but this is why it's very important to make sure you see a good injector and one who is honest about what you need done.