Scoop out a generous amount of drywall mud with a trowel.
Smooth the mud over the wallpaper bits by holding the trowel at a 45-degree angle. Start by moving the trowel downward, then side to side. Smooth until there are no visible lines in the mud. You will have mud left over on the trowel after you scoop away most of it -- you want only a thin coat.
Allow the mud to dry completely, which will take several hours to overnight depending on the climate.
Sand the dried mud with a piece of fine-grit sandpaper. Brush away excess powder with a dry paintbrush.
Paint the area with latex primer. Allow the primer to dry and paint the wall as desired.