Does neosporin work for reducing scaring after the wound has been almost healed or completely healed?

Not directly: Wounds and how they heal is directly related to intrinsic and extrinsic factors. The intrinsic factors that impact healing and scar formation include the depth of the injury (shallow wounds heal with minimal scarring), and your genetics. Extrinsic factors include mostly wound care - wounds that are kept greasy (vaseline) heal way better than those that form scabs and are crusted.