Well how about asking this way, were there any non-Civil War period artifact? If so, what were they? If the answer is, no, there were no other artifacts from a different time period, then it would more likely be of the period when you know people had a reson to be in that area rather than a random artifact lost by chance in the middle of nowhere that just happened to have been a Civil War camp site. If the answer is, yes, there were other artifacts, then what were they and what can they tell you about the time period they were lost in and the people who lost them.
Unless there is some glaring trait that requires it to have been made post-Civil War, I see no problem hypothisizing that it was dropped by a soldier at camp. Those medals were all over. Who would need one more than a soldier? I would suggest that in the Confederacy soldiers from the state of Maryland and state of Louisiana would be more likely to be Catholic, however a soldier from any state might be Catholic. If you can figure out what unit was camped there you might have a chance of identifying the former owner.