[wilf leek]

The reason you get a grind going into reverse is because there is no synchro on reverse.
Sitting in neutral, with the engine running and clutch out, means the gearbox internals are rotating at the same speed as the engine.
Shifting temporarily into 4th means that the synchro cones on that gear are braking down the still-rotating shafts etc in the 'box to a standstill, hence no crunch when you go into reverse.

I can think of three possible causes:

1/ You are rushing the change - the internals of the 'box have momentum which must be allowed to die away (i.e. all bits stop turning). If you dip the clutch, wait, say 5 seconds, and then put it into reverse (without knocking it into a forward gear first) does it still crunch? If so, go on to 2/ and 3/.

2/ Clutch drag - clutch is not clearing 100% with your foot right down on the pedal. Possible linkage adjust?? Hydraulics mismatched? Pedal adjust?

3/ Misalignment between bell housing/gearbox and the engine - means the input shaft is "tight" in it's bearing in the end of the crank, thus causing it to continue to spin the gearbox even with clutch fully disengaged.

I have to say that my own TKO will crunch going into reverse if I am too quick about it. Take more time and it's fine.

HTH