Thanks for the tip! It appears you have to remove them song by song. I was trying to do it per artist/album. Song by song is a huge pain in the ass. Especially when they've added literally dozens of albums to my library for free.
If you view the album where it gives you the tracklist of songs, you can delete them from there as well. Still more of a pain than deleting the whole album in one move, but easier than searching through every song in your library.
Edit since HN won't let me reply:
I see a "Remove from library" in your screenshot, which I assume does the same.(Edit 2: Didn't realize there were 2 images, so I'm wrong there) And I've never had anything appear in my library that I didn't add, so I cant really check, but you seem to be correct, since I have the same menu as I do in "Songs"
Edit again:
That looks like the menu I get when I hit the album's menu button, here's what I get when I hit the one next to the song while viewing the album:
but that isn't a Google-added one, so ymmv. (However the web interface lets you delete entire albums at once, so I'm not sure why you can't in the app.)