Fixing painted drywall
Joint compound will stick to paint with an eggshell sheen just fine.  

I am guessing they didn't paint the fresh patch with a PVA primer so the mud on the wall hasn't even been sealed yet.  Unless they put a lot coats of topcoat pain over the patch in which case they could of sealed it up with the more expensive paint.  But, regardless you can move forward just fine. 

To get the new patch though to blend in and not show up later, make sure you use a PVA or similar primer, they even sell some special paint for fresh drywall sealing (which is just a PVA primer anyway with a fancier name).  If you don't seal it with a primer, the patch and existing painted surfaces will each take the paint differently and still show.  PVA primer is sandable so you can take the primer out onto the wall a bit and sand your patch edges thinner without it peeling up.  The PVA will kind glue the thin compound together and bond it to the wall, especially so if you are using a "lite" topping compound.