Well... that at least explains the mystery, which is a good thing.

You'll probably want to keep the glued on part for now -- at least until the glass needs to be replaced. Getting those glued on parts off the glass can be a problem. Sometimes they come right off, but I've seen them break off a piece of glass in the process. If I track down a mirror I'll let you know. You'll be able to remove the mirror part and just use the other pin-holding part until what time you need to replace the windshield... then you can go back to stock.