A child support enforcement agency shall determine whether any obligor whose name was submitted to be displayed on a poster has met all the conditions of section 3123.956 of the Revised Code. If it determines that an obligor has done so, it shall give the office of child support notice of its determination. On receipt of the notice from the agency, the office shall remove the obligor from the list of obligors submitted by that agency before making the final selection of obligors for the poster.