Is there a way to clean walls painted with CHEAP paint?
More than likely they used cheap flat paint which does not clean well. Semi-gloss latex paint cleans very well. Unfortunately, the only thing you can do is to repaint the wall using a paint that is wipe-able, cleanable, and can easily remove stains and scuff marks like an interior semi-gloss latex paint in whatever color you choose. TSP is a chemical and it will eat away at your drywall if you use it on the wall.