EGA?

I was wondering if anybody out there has any info on this E.G.A. It appears to be off a garrison cover or maybe an old smokey, as you can see it has no fouled line nor a screw backing to attach it to the cover, it never has had a screw backing and the pin and clasp are original. I believe it to be pre W.W. Two. I have never seen one like this and I would like some help getting some history on it. It is the center piece of my Marine Corps memorabilia collection. Thank you.

Mike