Despite the name, even a washable marker may leave a spot or stain on carpet. Washable ink may be a little easier to remove than permanent marker ink, but the sooner you act before the ink has a chance to soak into the fibers, the easier it will be to clean. It may take more than one method to completely remove the stain from the carpet. Test your homemade cleaning solutions on an inconspicuous area first to ensure they do not discolor the carpeting.
If the stain just happened, you may be able to remove a bit of the ink before it sets. Blot with white paper towels or a white cloth without rubbing, otherwise the ink may spread. Continue blotting until no more ink comes up, using a fresh paper towel or cloth whenever the paper or cloth absorbs some of the ink. Switch to a damp white paper towel or cloth to absorb a bit more of the ink. Alternate between wet and dry cloths until no more ink comes up. If the stain is no longer visible, blot the area with a dry white cloth.
Pour some white vinegar onto a white lint-free cloth to lift the ink from the carpet. A white cloth, rather than dyed cloth, ensures that the cloth itself won't cause a colorful stain on the carpet. Blot the marker stains with the vinegar-soaked cloth, pressing down and allowing the cloth to absorb the washable ink. Lift the cloth to check for ink absorption, switching to another area of the cloth whenever you notice some of the color has transferred to it. Dab the area with a dry white cloth after the stain disappears to absorb the vinegar.
Dip a soft white cloth into a mildly soapy water, using a gentle dish soap or carpet and upholstery shampoo. Dab the spot to wet the carpet fibers slightly while lifting the ink. Avoid rubbing a small spot, as this may spread it around. For a large ink stain, rubbing from the outside towards the center of the inky area may help remove some of the ink. If the spot doesn't readily lift away, whip the soapy water until it is sudsy; apply the suds to the stain, allowing them to sit for several minutes. Blot with a damp white cloth, following up with a dry white cloth once the ink is gone.
Blot the marker spot with a white cloth after wetting the cloth with rubbing alcohol. Hold the cloth in place for at several seconds, applying the alcohol only to the stain, instead of surrounding areas -- this helps prevent the carpet fibers from absorbing the alcohol as it loosens the ink, which may cause some of the ink to bleed to surrounding areas. Continue dabbing and blotting, using a clean area of the cloth whenever the cloth itself becomes stained.