We can't tell who removed the tracks from the playlist. However, what you can do is copy the contents of the playlist into a new one, then tap Invite Collaborators and share the link with your friends to grant them editing permissions. The link expires after 24hrs, meaning no one else, but the people you've send the link to can add or remove songs.
You can also set the playlist to be private, so that the only people who can access it are you and your friends.
Hope this helps. Cheers!
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