Read your insurance policy. The company will pay for procedures that are covered, but most policies do not pay for cosmetic work. Sometimes it is a matter of interpretation whether some procedure is cosmetic or medically required.

Your orthodontist should be able to interpret your policy. If the amount of money involved is not large, it is probably best for you to pay it. But if it is a significant amount and you don't agree with the interpretations, you may want to have a lawyer look at the policy and try to arrange for payment by the insurance company.