Would Tricare pay for this procedure due to the hernia being removed or the resulting bacterial infection?

Thank you for sharing your question and I am sorry to hear of your TT healing issues.  Unfortunately as the insurance covered the cost of the hernia, which was not disrupted, it is unlikely that they would cover the cost of a procedure for the overlaying skin.  It is difficult to make a recommendation without seeing photographs but hopefully local wound care alone will leave you with an appropriate belly button appearance.  Best wishes.