Different model years apparently have different mounting systems.
On the 2007 it is not possible to remove the strap without removing the saddlebag mount.
Gonna try removing ther strap entirely, have heard of many claim the seat will occasionally work its way loose without the strap, which I can see happening, My seat mount screw often loosens.
If you have a thumbscrew, get rid of it. Replace it with the properly sized socket head screw (allen), preferably stainless, and a stainless lock washer. Tighten it with an Allen wrench kept in your tool pouch. Never had an issue with mine coming loose after doing this, and thieves don't often walk around with Allen wrenches in their pockets.
I don't know why you'd have to remove the saddlebag mount to get to the strap screw...something ain't right. The strap is useless anyway, as most BSR's are virtually sitting on top of it. It MIGHT be useful on a bike with no sissy bar or backrest for the passenger to keep her from falling off the back...otherwise, I don't think I'd recommend to my BSR that she hang on to a strap on the seat if the bike went down or tried to eject her in a crash....her hands are too useful to lose one.