Wipe the stained area with a soft cloth dampened with acetone. The acetone cleans the upper layer of the stain, and makes it easier for a poultice to draw out the rest of the oil or grease.
Mix baking soda and water into a thick paste. The paste should be thick enough to spread, similar in consistency to toothpaste.
Spread the baking soda paste onto the stained area. Make sure the poultice is 1/4 to 1/2 inch thick. If the paste is not dense enough to hold that thickness, add more baking soda.
Cover the baking soda poultice with plastic wrap, and tape the edges to the marble.
Leave the poultice in place until it is dry. It can take as long as 48 hours for the poultice to dry.
Remove the plastic wrap, and wash the area with mild soap and water.
Dry the area with a soft cloth. Repeat the poultice if any of the grease stain remains.