When you say you've seen it both ways do you mean on originals or on contemporary rifles? If you go to the Virtual Library & Museum - Indexed by State on the forum homepage, you will see that all but one of the Tennessee rifles use screws to secure the trigger guard with the exception being Bogle rifle which I feel bears some Virginia features. Alfred Boggs even used screws on his silver mounted rifle. Now, of course, not every Tennessee rifle is represented there but the law of averages says screws.
And use an English lock too. J.D.