A frum dentist has a professional relationship with a goyish specialist where the specialist comes in monthly to do his patient’s root canals. If the specialist does not perform the root canal properly (he left a piece of the nerve in the canal and the tooth and bone got infected afterward) and the procedure had to be done a second time by another specialist. Does the frum dentist have any financial obligations? The patient is claiming a refund of the $1,500 fee that he paid for the first root canal to the frum dentist.
Because this question involves two parties, the answer is only given by way of advice and general background.
The question implies that the contract for performing the root canal was made with the Jewish dentist, who sub-contracted a non-Jewish dentist to do the work (there is no direct contract between the patient and the non-Jewish dentist). It thus follows that the claim for a refund must be directed at the Jewish dentist to whom the money was paid. However, the claim is only valid if the treatment — as the question states — was not done properly/negligently. It would then be the dentist’s responsibility to arrange the matter with the specialist.
Of course, there might be other details that would further affect the case.