Remove the All-Clad pan from the heat, and pour club soda in the pan while it is still warm. Add 1 tbsp. of baking soda to liquefy and loosen burnt-on cooking oils or food. Pour the liquid out into the sink.
Fill your sink with warm water and dish detergent. Submerge the burnt all-clad pan, after it has cooled, in the soapy water, and let it soak for up to one hour to loosen burnt-on food remnants. Rinse off the soap, but do not dry the pan.
Pour a powdered stainless steel cleanser that does not contain chlorine bleach, such as Bar Keeper's Friend or Bon Ami, in the pan. Rub the powder in a circular motion over the burn marks with a nonabrasive sponge or towel to create a paste. Rinse and dry the pan.
Cut a lemon in half. Rub lemon juice onto the burn marks with a soft towel or sponge to buff the marks out and restore sheen in the All-Clad pan.