Can you add the tweet directly to the database with a blank tw_id? The twitter check could first delete all tweets that are null, to prevent duplication issues.
If you can add a blurb into the readme about the deletion thing that’s probably good enough. Possibly add something about deleting it from the database.
Or you could add a “delete a tweet” option to the admin interface. If you include documentation on how to find the tweet id you won’t need to worry about a big interface.