Only storing part of a DB

I've got a DB that is controlled by a third party and do not want to store most of it. We have added a couple of triggers (yuck) to various tables so we can extract any required data we need. All I really want to put in source control are these triggers.

I've linked the DB to SQL Source Control as normal and only ticked the the tables that contains the triggers I want.

My question is, is there any way to set the source control to stop showing the rest of the database in the Commit changes tab? Ideally, I'd like a way of telling source control that this current status is a baseline, and only to offer to commit changes from this position.