I think that LJ is correct in that you may have to take back the piece.
However, I would try the iron first. Edge banding for veneer and even laminate is sometimes bonded using a heat activated glue. Even the typical white or yellow carpenters glue responds well to heat bonding. Here's what you should do -- heat an iron to its hottest setting (no steam!)and lay a thin clean dish towel flat over the veneer with the lifted edge. Then put the iron on the dish towel and move it back and forth, pressing hard. After it has cooled somewhat, lift the dish towel and see if this works.