I have some nice medium and dark colored damask soft cotton tablecloths and napkins. The darker and medium range colors seem to show the food grease stains worse than white linens do. I have White Wizard and Fuller Brush's product called Stain Blaster, which is a soy derivative cream and comes in a jar. The White Wizard cream is less effective than the Stain Blaster. I wet the cloth thoroughly, rub in the product very well and then seal in a plastic bag for a couple of days of letting the product soak in to (hopefully) let the magic happen before washing.
So, That's what I do. The Fuller Brush Stain Blaster does not fully remove the grease spots on the first try. But by the third go around I'm pretty satisfied that the stain is gone. But the Fuller product is about $20 for an 8 oz. jar. And it probably takes about an ounce to totally deal with a large grease stain on a tablecloth.
Do you have any other products or hints or techniques that will work for grease stains on medium colored or dark table linens? Bleach is out of the question.