Wipe down the surface of the stoneware with a damp cloth.
Pour baking soda into a small bowl or cup. Add a little water and stir up the mixture to create a paste like liquid.
Wet the sponge with water and dip the sponge into the baking soda/water paste.
Gently rub the paste onto the scratches. Let the paste sit for a few minutes. Wipe it off with the sponge then rinse the stoneware with plain water. If the scratches persist, proceed to Step 5.
Spray or sponge on a small amount of commercial stoneware cleaner onto the stoneware surface. Allow it to sit for a few minutes and then rinse it off. Repeat as needed until the scratches are gone.