Whooah, I dont even understand several of these answers! Have you guys been hitting the beers???
Yes, what kind of paint is on the wall nearby. Be carefgul using sponges or Magic Erasers. ME's can probably remove the grease but also may remove the semi gloss finish. Try ONLY in a small spot and if it looks all right, go ahead. Use a good de-greaser. There are many out there. One of my customers likes 409. It DOES work well but I find it too harsh on my skin even wearing gloves. Plus it smells icky.
Good luck with this one.