Cover the scented oil stain with baking soda. Leave the baking soda on the furniture surface for 10 minutes to absorb the oil.
Brush the baking soda off the furniture surface with a soft brush. Discard it in the trash.
Fill a small bowl with 1/4 cup dry cleaning solvent and 3 tablespoons Fuller's Earth. Stir the two ingredients together to create a paste.
Smooth the paste over the remaining scented oil stain. Leave the poultice on the wood until completely dried. As the poultice dries, it draws the remaining stain out of the wood.
Remove the dried paste with the scrub brush. Discard the dry paste in the trash.
Moisten a clean cloth with wood cleaner appropriate for your furniture surface. Buff the furniture with the cleaner. Dry the surface with another cloth.