Hi Frances! This is how we designed Briefcase to work. Because people use it for back up and to move data from one server to another, we don't want it to delete data that is deleted from the server.
One option you can try is to select a different Briefcase storage folder and pull data to that storage folder. If you upgrade to Briefcase v1.8 another option to try is to export data from a particular date range (e.g., after the date you deleted forms). Are those good solutions to your problem?
Oh, and when you get a chance, please introduce yourself here. I'd also encourage you to add a real picture as your avatar because it helps build community!