I have no idea what this thing looks like but from what say it may be a small piece of eccofoam. This is a closed cell foam used as a packing material. Closed cell just means water won't penetrate it and it won't flake like styrofoam. As for bonding it to the door I'd try roughing the door surface with coarse sandpaper and using silicone seal. The foam is easily cuttable with a bandsaw or even a sharp kitchen knife. Not sure if this will work, just an idea.
Al