Use a fine-grained sandpaper to gently scrape away as much of the scorch mark as possible.
Vacuum the area around the burn to clean up the sanding residue. After vacuuming, you may find that more of the burn mark has been removed than you realized.
Mix 1 teaspoon of hydrogen peroxide into 1 cup of water. Especially for darker carpets, test this mixture in an inconspicuous location before using it to clean your carpet. If you notice discoloration, use a mixture of liquid soap and water instead.
Dampen a cloth in the mixture and dab at the remaining burn mark, working from the outside of the mark toward the center. Continue until the stain is fully removed, then dampen a fresh cloth with water and rinse the area.
Blot the area with a fresh cloth until the carpet is dry.
Vacuum the carpet again to fluff the carpet fibers.