A gun is worth what someone will pay for it. How hard you look for a suitable "someone" is the question.
I assume you have done your homework. The first '03s actions were not of the best treated steel and tended to crack and become unsafe... Supposedly Uncle Sam managed to "recall" all these actions and swap them for a later version "double heat treated..." If you have an action that was missed, unlikely, it could be very valuable. 1919 suggests a double heat treated... Safe. The 2 groove and date in '44 suggests that the gun was redone for the government during WW II as a trainer, drill rifle, guard rifle... etc. Combat soldiers got Garands by then, hopefully. Many of the 2 grooves shoot remarkedly well. If the wood is original, the plastic finish can be taken off. I would seek the advice of someone who works with wood. Brownells.com for instance. There is probably a solvent that will strip it without the work of sanding it off. And an oil finish or none at all would be o.k. to a collector. As said, many sources have the metal parts. The end for the foreend top and a sight, maybe. I would look into the holes carefully, research type "look into." Some guns were drilled for various "sniper" sights. More likely for a civilian use, but if it is sniper... more value to a collector. And if you can pick up the sight and sell the gun with it on, more value...
As I said, how much work do you want to do and how hard do you want to search for a qualified buyer. Shotgunnews.com beats the local paper for anything but tomato stakes every time. It has been long enough that '03s are getting a little scarce... I would work a little to find a crazy collector. luck.
