The rear strap is there to keep the bike from bouncing around. Just get the strap "looped" to keep the wheel near the tray. I've driven a lot forgetting or not having the rear strap (hours of driving at a stretch, period of months without a strap).

The only time you'll get a lot of pressure on the strap is if the fork mount doesn't hold (loose, breaks, etc). At that point the bike is hanging down from the rear wheel. The rear strap being looped will keep bike on car. You'll probably have other concerns at that point.

cdr