This can be done 2 ways.
Deleting the entire playlist
- Music/Playlist/Transfer (icon) (the up and down arrows in the upper right corner) = select the playlist and delete
Deleting songs on the playlist
- Music/Playlist/Specific Playlist/Transfer (icon) (the up and down arrows in the upper right corner) = individually select the songs you want to delete from the playlist. This will delete the songs from the playlist only.