Just noticed an odd spell I'd never seen before when checking my spell list after leveling up. Turns out it's a homebrew item, but I haven't added it, and it's not by anyone in my campaign. No other homebrew items (equipment or spells) that I haven't added are showing up in my list. 

Edit: there are one or two other spells showing up that shouldn't be there. Ray of Frosting is one. I tried turning off a couple "sources" in my character sheet but they didn't go away, they're definitely in the Homebrew source. Finally just turned that off, and the homebrew item in my inventory is still there, so I guess the workaround is to just turn on Homebrew only when you need to add something. But if you need to leave it on this could present a problem as you'll have no idea what spells are really regular spells that should be available, without looking up every single one you aren't familiar with...

If you look at the expanded details of a spell in the editor, or in the sidebar in the character sheet, you should see a line that says 'Source:' right with all the other basic stats like duration, range, etc. It'll have an abbreviation for a book, and a page number. If you don't see this information, but instead see a line that says 'Version:' then it's homebrew.

Someone in that campaign has those spells added to their collection. All homebrew in everyone’s collections are automatically shared within DDB campaigns.

I presume you are playing a artificer, Klarich, druid, or paladin. Am I correct?  The way those spells were designed must have your subclass on their list, and for those classes, any spell attached directly to a subclass automatically counts as “Always Prepared.” All Homebrewed spells can easily be identified on a character sheet by their inclusion of a “Version” field, even if no version designation is entered. Official spells do not have that field.

Once something has been added to a character sheet, it will remain even after the source has been toggled off, or removed entirely.