Assume the car is at a full stop. With the clutch disengaged the input shaft and countershaft are still free to turn from friction as long as the trans is in neutral. As soon as you engage a gear everything in the trans stops turning until the clutch is engaged.

So with the car stopped, shifting the trans into reverse should do NOTHING since nothing is turning - maybe just a little gear clash as you engage reverse but nothing more and it should not be continuous.

So, if you are getting a continuous noise then I'd suggest looking outside the box (no pun intended). Its strange that it would only do it in reverse but consider the throwout bearing - which only turns when the clutch is disengaged.

The only other thought is that reverse is not fully engaging at the teeth are grinding but in that case you wouldn't be able to back the car up at all.

Check the easy stuff first - outside the box!