Is it permissible to go back on the decision to abandon cosmetic surgery for the sake of Allah, and to return to it after it has become clear that a female doctor can perform the treatment?

If the purpose of the orthodontics is to remove a defect or avert harm, then it is permissible. However, if it is merely for beautification, then it is not permissible. There is no objection to abandoning its ترك (which likely means "abandoning the non-permissibility" or "abandoning the position of leaving it") if it was permissible in the first place. Nothing is required unless an oath or vow has been uttered.