How wet was the towel if just damp enough to wipe off the glue it should be ok, don't think it will come apart at the layers unless it was just soaked with water, if still have some glue on it might try using whats call a cabinet scraper to clean the rest of the glue off after its dried. If it does still warp or cup a little use equal clamping force across the whole piece to glue it down, might even use a pin nailer if you have one, it uses very small wire pins it shoots made for tacking wood together for glueing and such, will hardley see the pins they are about the size of a needle.
