I have a small space that a previous owner painted in a red eggshell. I believe that all of the original plaster in this space was replaced with drywall if that matters. When I wipe them down with a damp washcloth (no soap) the white cloth comes away with a pink tint. I don't feel any obvious roughness that indicates that the walls were dusty when painted, but some of the paint obviously comes off.

I want to paint this space in a lighter color, so I will definitely prime first. I still worried that the new film may fail given the current behavior. Any suggestions for preparing the surface?