Blot up fresh Chapstick using white paper towels. If the Chapstick has dried, gently scrape off the hardened red gunk using a spoon.
Moisten a white terry cloth with 1 teaspoon of dry cleaning solvent. Tamp the remaining red Chapstick blemish with the solvent until no further red residue transfers onto the cloth.
Inspect the carpet for lingering Chapstick. If any red gunk remains, pour 2 cups of warm water into a cleaning bucket. Mix in 1 tablespoon of both liquid dishwashing detergent (non-bleach) and white vinegar.
Dampen another terry cloth in the homemade solution. Tamp the remaining red Chapstick residue until it dissolves.
Moisten another cloth with cool water. Blot the carpet until the homemade solution is completely rinsed out.
Tamp the carpet with a dry white towel to absorb moisture.