Put a lock on it and don’t worry about the phone company or the home warranty.
If you look at that box carefully, you’ll probably see that the “box half” (as opposed to the lid half) of the locking point is screwed onto the box with a recessed and/or odd-headed screw. Rest assured that the phone guys have the corresponding tool.
Also, unless there’s a problem that you report with the line, odds of anyone opening that box on any sort of schedule are never to none.