Purchase an art-gum eraser, and rub it lightly over the smudge to remove it from the wall. Continue rubbing carefully with the eraser until the smudge is gone. Stop rubbing before you remove any paint or make the smudge worse.
Mix baking soda and water in a dish to make a thick paste. Dip a wet cleaning cloth in the paste.
Apply the paste gently to the wall over the remaining eraser stain. Rub gently to remove the smudge but not the paint.
Wipe away any remaining baking soda paste from the wall with the damp cloth.