Attack the stain as soon as possible. The longer the stain sits on the fabric, the less likely it is that you will be able to remove it.
Wear cleaning gloves. Avoid exposure of your skin to marker ink and rubbing alcohol, if possible, so your hands will not sting or get stained.
Cover a surface with paper towels. Place the toy on top of the paper towels. The towels will catch any runny liquid from the cleaning process. If you can get at the stain from underneath -- if the wrestling toy is a puppet with the inside of the fabric exposed, for example -- place the stained portion of the toy face down. The paper towels will absorb some of the ink.
Pour rubbing alcohol onto the sponge over a sink. Soak the sponge thoroughly. Ring the excess alcohol from the sponge.
Blot the stain with the sponge. Every few seconds, shift the sponge so that a new, clean spot of the sponge absorbs the stain. If you are able to get at the stain from the inside, blot the stain from the inside and not the outside. Continue until the stain disappears. Rinse the cloth with cold water and allow to dry.
Cover a surface with paper towels to absorb excess nail polish remover.
Put on cleaning gloves. The gloves will protect your skin from irritation in case you expose your hands to the nail polish remover. The gloves will also remove any risk of inking your hands.
Soak a clean sponge with the the non-acetone nail polish remover over a sink. Ring out any excess.
Apply the nail polish remover directly to the stained plastic with the sponge. Wipe the stain but do not press hard. Reposition the sponge whenever it becomes stained and apply a clean portion of the sponge to the stain. Repeat until the stain is gone. Rinse the toy with cold water and dry it with a clean paper towel.