I believe some folks believe this will bring good luck but it may also tie to the old idea of leaving "something of yourself's" at a grave. Jewish people leave stones when they visit a grave so maybe this is similar. When I visited McGavock Cemetery I didn't see any or if I did I don't recall it. Maybe somebody just wanted others to know they care?
For what it's worth if anybody wants to leave me anything please do so before I die and it would mean a lot if the money was the folding kind... Yankee script of course!
P.S. McGavock is a really special place. Tell us more of your visit!