85 BRAT. Starting out by backing up there is a grinding noise that sounds like worn brake shoes against the drum, checking those they are good. the cv joints are original (103K miles) and no visable sign of grease leakage. No driving problems not in 4WD although there is constant noise from the rear. Also any way to reduce the sound coming from the fuel pump mounted to the frame?

Aside from the actual shoes in the drums, I would inspect all the springs to make sure none are broken / hanging off.

+1 for the broken spring.

Could a bad bearing cause the noise?

If it was bearings you should hear it all the time, not just backing up.

Check engine and trans mounts. The torque load on them differs between forward and reverse.

 

The exhaust is supported by a bracket on the trans, so if trans mount is bad, it cold let exhaust rub on something while reversing that it wouldn't rub on going forward.

 

Just my .02.