Could be the parking brake, or a spindle bearing.
Can you have someone listen to it from outside, on both sides, to determine if the noise can be narrowed down to a particular area?

Hey Joel,

Try applying the emergency brake lightly as you roll backwards, and see if the scrape noise changes. That might help pin-point the source. Seems like if it does change it, then the brakes would be the first place to investigate.
Another possibility would be the ujoints in the halfshafts. They can make scraping noises when they get dry.

I had a scraping noise on my 75 last year. it was the yoke clip in the differential had fallen off, so the yoke moved in and out of the differential and that caused the U joints on the half shafts to come in contact with other parts. Had to do a toatl differential rebuild.

I beleive you can check the yokes, with the car jacked up grab the bottom and top of the rear tire and rock top to bottom if there is movement in and out the yokes are worn. Thats how mine was discovered.

Me and a friend gave it another listen today.

The side yokes on my '78 were worn pretty bad with just 50k on her. One side was worn right down to the "C" clip. Much more and it would come off. I read poor metal quality those years. Only opened it cause the cover and seals leaked. Nasty looking oil with them metal grindings mixing in. Don't remember any noise in reverse. But the wife says I don't hear much anyway.

And I'd have a pretty nice Vette if I was deaf, dumb and blind!