Metal detecting and found a Marine Corps EGA eagle globe pin. It has a earring locked down on the backside of it. Would they back then do that to remember there sweetheart when off to War.

Yes, they do that to remember their sweethearts when off to war because the earring is not part of the Marine Corps EGA eagle globe pin.

Explanation:

even the women recruited in the US Marines do not have earrings attached to their Marine Corps EGA eagle globe pin.

Note: When the Marines began recruiting women reservists seven months ago, the Corps decided that its uniformed women would carry no telescoped name like WACs, WAVES or SPARS; they would be Marines. But "women Marines" is a lip-twisting phrase. "She-Marines" was frowned on, too. But the eventual development of some unofficial nickname was certain. Last week the Corps had it: BAMs. In leatherneck lingo that stands (approximately) for Broad-Axle Marines.

women should have the same rights as men