You can delete tables, but only one by one, @Matthew Benesh.
Check it out and you'll see a delete button:

If you have many to delete, it'll take a while. Once you check them in, they'll be gone.
Naturally, you need to ensure that deleting those tables won't create problems down the line (transforms, allocation lines, lookups, etc.)
Unfortunately, Apptio/TBM Studio offer little help, beyond finding what tables relate to the selected one (but not the nature of the relationship).