Start the engine and put the transmission in first gear. There should be no grinding at all. Put the transmission in neutral, and without releasing the clutch pedal keep it in neutral for 10 seconds. That's 10 seconds in neutral with the clutch pedal all the way to the floor. Then put the transmission in reverse.
If it goes into reverse with no grinding you have no problem at all. If it does grind your clutch is dragging, possibly the pilot bearing has failed or the clutch disk is warped.
There's nothing unusual about the transmission grinding if you go directly into reverse from neutral. That's because, unlike all the forward gears, there's nothing on the reverse gear to keep it from grinding. I got into the habit of putting my transmission into any forward gear before putting it into reverse just do I wouldn't have to hear the noise.