Imagine this:
Hey, nice gun, where'd ya get it?
Um, from my (family member).
That's what I thought. Is it registered to you?
Not really.
Hand it over.
I've been to only two ranges. Both had almost the same BSF (badges per sq ft) as a 10-4 donuts shop. That one was across the hiway from the Sherf hive probably explains that.
Although you never know, I don't think you really need to worry about that.
First, unless people are pretty into both history and firearms, they're probably not going to know what you've got (unless we're talking something like an MG, and then there
are certain legal things you need to worry about) - the hot items these days are space guns, and your average person at a gun range, except for somebody working for the BATF, is probably not going to know a Springfield or an M1 from a hunting rifle.
Second, there are plenty of both perfectly legal (not to suggest that you're not entirely legal - but I don't know that for a fact) military-looking weapons floating around, and there's no reason to suspect anything different with yours (again, unless it's machine gun or something like that). For instance, the group that took Springfield Armory's name makes clones of both the Garand and the M-14, and there are some other companies out there making at least the latter (and I think the Garand too, but am not as sure).
Third, even if someone asked and you told them the complete story, the reaction would probably be "cool," except from the world's biggest jerk.
But, here's what I'd be concerned about (and I'm not even sure how realistic it is): depending on what you've got, it might have some pretty serious value to it (from a variety of perspectives, including a lack of traceability to a particular person). Sometimes word gets around.
So, legal issues aside, I just wouldn't advertise it.