Put a dab of white toothpaste on a soft towel. Do not use gel toothpaste; it does not have the same effect. Rub the toothpaste on the water circle, using firm but gentle pressure, until the mark disappears.
Fill the bottom of a bowl with water. Mix a few dashes of baking soda into the water. Use a towel to rub the baking soda on the water circle. Keep rubbing until the circle lightens and disappears.
Put mayonnaise in a bowl. Add ashes, such as those from cigarettes or a fireplace, if you have them on hand. Apply the mayonnaise to the water circle and let it set overnight. Wipe the mayonnaise off with a dry towel. The water circle significantly lightens.