Before you even submit the cards, you should send that email to the review team - military insignia use for commercial personal profit are a real no, no on all sites. So, it will depend on WHO gave you permission and exactly WHAT the permission was for I'm sure.
 
In other words, receiving permission to use a military insignia for a PRIVATE customer requested greeting is often acceptable because it's not in the public marketplace for anyone to purchase. I'm not speaking on behalf of GCU only as an artist who has worked with and sold on POD sites like GCU for almost 10-years. The only difference is that GCU stops trademark issues at the submission door, whereas most of PODs will at some point terminate the product(s) you've created once someone finds them and reports them.
 
So, start by sending a note to: cardreview@greetingcarduniverse.com explaining your request and including the permission - go from there. Then you are not wasting your time or theirs.  That's what I would do, anyway.