AKICILJ: repairing cardboard tiles

[zwol]

I have a bunch of cardboard tiles (specifically, Carcassonne game pieces) on which tea was spilt, and so have come slightly delaminated at the edges. Right now they're mostly okay but it looks like with continued use they might get seriously frayed or even split. Can anyone suggest a way to repair them or at least stop further damage? The only idea I've had so far is applying dilute Elmer's glue to the edges with a brush, but that might only make things worse.