Can pulling a car onto a tow truck backwards while in gear damage the manual transmission. The car now pops out of gear in reverse and grinds when going in second gear only.?

Yes, pulling a car onto a tow truck backwards while in gear can potentially damage the manual transmission. If the transmission is engaged while being towed, it can cause undue stress on the internal components, leading to issues like popping out of gear or grinding when shifting. The symptoms you describe suggest possible damage to the synchronizers or other internal parts of the transmission, which would require further inspection and possibly repair.