Well, you have beaten me.
I think I could fix it if it was my Library here, but only by doing some dodgy stuff with the Library, involving exporting all Playlists, deleting a file in the Library, re-importing the Playlists, then re-arranging them again the way they were before. That would entail some risk that I wouldn't get my Playlists back the way they are now, but I think it would work. Library Backups would be essential.
What is strange is:
1. That the Playlist Group (folder) was created by MC. I've not seen that happen. That implies it was supposed to be an internal, (possibly hidden) Playlist Group that MC was using for something, and hence should manage itself.
2. That the Playlist Group (folder) doesn't appear in Standard View. All Playlists and Groups appear in Standard View, except maybe internal MC system Playlists. But why would they appear in Theatre View?
Could the Playlist Group have originally been named something else, and it accidentally got renamed? If it was marked as a System Playlist, like the "Recent Playing Now's" Playlist Group, it might prevent deletion from Theatre View. But I'm not even sure MC has such system Playlist Groups.
Well, actually there is no delete function for Playlists and Playlist Groups in Theatre View. All those delete functions work on files, not the Playlists and Playlist Groups. Hopefully you haven't accidentally deleted some files while testing the delete function. I removed a few from my Main HTPC Library unintentionally, and will now need to do a Library Restore on my HTPC. Ooops.
Maybe someone else can help?