AGAIN: Do NOT use glue. Glue is water-based usually and when wet or damp, the glue will un-glue and re-glue to anything similar, like another glued piece of cardboard.
What you probably should do. Preserve Carc-Tiles with a spray on clear coat. I heard about a product in a video, Rustoleum Ultra Cover Matte Clear. It tends to coat but not obscure artwork. I suggest that you experiment with like tiles to see a result. This same video also noted that the edges of cardboard may not be fully protected as the front. A brush-on version of this product work.
Great Luck