Sweep up loose debris from the scuffed ceramic tiles using a broom.
Squirt the scuffed areas of the ceramic tiles with all-purpose water-displacing lubricant. Don't soak the scuff marks, just moisten them.
Rub the lubricated scuffs with a nonabrasive sponge. The solvents in water-displacing lubricant make scuff-removal simple, so vigorous scrubbing is generally unnecessary.
Saturate a cloth with water. Pour a drop of mild liquid detergent onto the cloth.
Wipe the lubricated ceramic tiles with the soapy cloth. Clean the tiles well, thoroughly removing the water-displacing lubricant.
Saturate another cloth with water. Wipe the previously scuffed tiles to rinse off soapsuds.
Wipe the wet tiles with towels. Remove all moisture to avoid slipping.