Per the owners manual included with the car
"To engage reverse, while at a complete stop, first put the car into 2nd or 3rd gear and then while still depressing the clutch pedal, shift into reverse, otherwise repeated use may damage the transmission".
The reason is your shift into a forward gear will momentarily stop the spinning secondary shaft holding the gears. It is spinning due to the input shaft spinning and the viscosity of the gear lube is causing the 2nd shaft to turn. This allows you to engage reverse without grinding. If first is also grinding, either yoiur clutch is out of adjustment or your 1st gear synchro mesh is wearing out. Usually 2nd is the first gear to lose its synchro since it gets more shifts than any other gear and first is typically engaged with the car standing still. A worn out clutch disc will improve the above situation rather than aggregate it since the disc gets thinner providing greater disengagement gaps.
Now, my last thought would be to as suggested above, try changing the lube. I'd bump up to a full synthetic that will flow at the lower temps. No viscosity thickening like the mineral based oils when the temps drop. It also offers improved cushioning when hot. Your shifts will be smoother while extending the life of your synchros and bearings. Good stuff!
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My Christmas present to ME! Bought Sat 11-30-2013. 72, 350 4 spd, Silver with blue interior...Can't you just hear Pablo Cruz playing in the background?