Grease stains on your walls and ceilings prove particularly problematic in the kitchen, where the splattering of food and oil leaves stubborn marks on your painted surfaces. It is important to remove as much of the grease stain as possible, though--especially because you can't simply paint over a grease stain. The grease will soak right through the new coat of paint where it will appear all over again.
Blot the grease stain with dry paper towels or a soft cleaning cloth to remove as much of the grease as possible. Do not rub the stain, as this could make the grease stain larger.
Mix vinegar and hot water in a bucket or container in equal concentrations and apply to a clean cloth or sponge.
Scrub the painted wall with the sponge, working the vinegar solution into the stain so that it can break through the grease. If the painted wall is textured, use care when scrubbing the surface so you don't damage the paint.
Rinse the wall with a sponge soaked in clean water once the grease stain has been removed.
Pat the wall with a dry cloth and allow it to air dry completely.
If you can't remove the grease stains from the painted walls, consider repainting the wall to eliminate the grease marks. Before painting, the wall will need to be primed--a step that will prevent the grease stain from showing through the fresh coat of paint.