I cannot find a policy by Anthem (or any other insurer for that matter) that states an external cause code is required to bill CPT 31591.
I suspect, however, that since 31591 is a reconstructive procedure (repair of the larynx), that the insurance payer may be classifying this procedure under the general requirements for "reconstructive" versus "cosmetic" surgery. In these cases, the external cause code validates the presence of an injury or trauma and indicates that the reconstructive procedure is to restore function or help return the patient to a pre-trauma state (a covered service). While most insurance carriers focus on liposuction, rhinoplasty, and other more common cosmetic procedures, there are insurance payers that lump all "-plasty" procedures under the cosmetic surgery policy, unfortunately.
In your case, I would contact my provider relations representative and ask for a copy of the policy that states you have to use an external cause code to bill CPT 31591 (or any other official guidance they can provide) since there is no policy currently listed on Anthem's website. If they are not able to produce anything, then ask your representative what you need to do to send the claim back through for reprocessing so that it does not get denied again on the basis of non-existent criteria.
Hope that helps!