Can I Recoup Damages From Poor Quality Work Done By A Licensed And Insurance Contractor? 
Your best option is to file a claim against the contractors insurance company . There may be coverage under the products and completed operations portion of the contractors policy potentially . You can check with the contractor license board to see who the contractor was or is insured with and then call the insurance company to request a claim be opened . The insurance carrier would then have to investigate for coverage . Even if the contractor no longer has the insurance or is in business if there was an occurrence policy with no sunset you may have a recourse . 