Who knows, maybe a greek guy hid his gold reserve inside the stock, and you are not likely to find out due to you never removing the grease ... seriously, I see no reason why this would mummify wood in an area where anyway nothing can go to it. But doesn't matter anyway, whatever you prefer.
I’m not sure what I’d do. I might just leave it. I have a cmp Greek return 1903 and my hole was empty. If you decide to go further, I would take the butt plate off and have a better look at it. It might be grease the soldier packed in there to lube the rifle? Or maybe there’s something behind it? You could probably take a large drill bit in your hand, and just turn it with your hand (not on a drill) to pull the grease out.
Do you live in a warm climate and plan on shooting it during the summer?
I personally would only take it out if it’s a shooter. Nothing as annoying as seeping cosmo on your shoulder on a hot day. If your not shooting it, leave it alone it’s kinda interesting.
I agree with GColloton with approach to removal. Plus where else are you gonna keep your Cleaning kit!? Uncle Sam wouldn’t want a pile of Greek poopoo hiding in there. Hehe
It's a greek return so by definition a shooter, unless it's a LN, in which case...shrug.
Take the action out of the stock and remove the buttplate.
Heat is your best bet. Cover the butt with some plastic bags, then immerse the butt in hot water, in the bags, so the heat transfers to the wood but doesn't get it wet. When heat has softened the cosmo, pull it out of the hot water and work it out of the hole with a pistol rod & patches. It may take awhile to transfer heat through the wood to start softening but the working time will be longer too with good hot wood.