You can check the current adjustment by putting the remote in reverse. You'll either have to have the engine running, or (with the engine OFF and spark plug wires pulled) have someone turn the prop while you're shifting.
If the shift arm is not all the way to the back of the slotted rail that it rides on, you're probably not far enough back for full reverse engagement.
And Yes, you disconnect the linkage that holds the shift cable's barrel adjuster and turn the barrel one way or the other to make your adjustment. Ideally, you want the cable pushing into full Reverse with just a bit of pressure. But you have to check your Neutral and Fwd positions after doing so, to make sure they're still in adjustment.
Note that with reverse gear grinding for that long, likely the shift clutch and cogs on reverse gear are damaged. You'd either need to dismantle the L/U, pulling the bearing carrier/reverse gear assy and the propshaft/clutch assy, and replacing any worn/damaged parts. Also you'd want to take a hard look at the shift cam and plunger, and renew those if there's any wear.
It might be simpler and cheaper to find a 50hp parts motor on your local Craigslist. There's a number of them on mine (Seattle) right now, for $100 or less. It'd cost you more than that to buy all the parts required, and the special gearcase tool to remove the gearcase threaded "nut" which has to come off before pulling the bearing carrier.
If your motor was used in fresh-water only, you'd have a pretty good chance of the L/U coming apart easily. But if you have a Salty-Dog, I wouldn't mess with it. Just get a good used L/U and away you go!
Maybe Good Fortune will shine on you and the adjustment will fix the problem, if not, Craigslist (or eBay if you're fortunate enough to find a deal on a L/U) is the answer!
HTH & G'luck.........ed