Pour milk and cornstarch into a small bowl. Stir the two ingredients with a spoon to create a paste.
Apply the paste to the Mr. Sketch marker-stained carpet. Allow the cornstarch paste to dry on the carpeting. Remove the dried paste and any absorbed marker stains with a vacuum.
Pour warm water into a small bowl. Add dishwashing detergent and white vinegar and mix.
Saturate a sponge in the vinegar-and-detergent solution. Squeeze it to remove excess moisture.
Dab the marker-stained carpet fibers to moisten them, then press a dry cloth onto the carpet to absorb ink. Repeat this process to remove as much of the Mr. Sketch marker stain as possible.
Dampen a clean cloth with water. Blot the carpet to rinse out the vinegar-and-detergent solution.
Tackle any remaining marker stain with a cloth dampened with rubbing alcohol. Sponge the carpet to remove the rest of the ink. Blot the carpet with a moist cloth to rinse it.
Allow the carpeting to air-dry completely.