I know that this thread is a little old but I just found it after searching.
It turns out that I may have the same problem. It started when I noticed that once all my doors and liftgate was locked, that the glass portion of the liftgate was a little loose. At first I thought it was something blocking it, but checked the lining several times and it wasn't anything there.
Upon further investigation, I noticed that the loop/handle portion of the glass liftgate was loose. So I pried back the plastic a little, thinking that it might've been loose screws, only to find that the two studs seems to have rusted off to the point where the loop portion seems to be sitting inside the plastic trim panel. It looks exactly like the OP's images of the metal stud plate.
The outside FORD decal plate doesn't have the cosmetic crack problem that these cars are known for. The glass itself is perfectly fine and the liftgate glass still latches (as of now). It catches and locks but I'm not sure how long that'll last. I havent taken off the interior trim panel yet because I'm not sure if it's holding things in place and I don't want to make matters worse by removing it.
I was looking at the metal plate that holds the two studs and it seems that it might be possible to adhere it to the glass in order to make the hook/metal plate portion stay in place well enough for the hook to latch properly. Is it really that easy? I don't want to (and can't afford to), spend money for a whole new back glass, when its perfectly fine otherwise. I have an 02 with about 187,000 miles on it, so I'm not sure its worth it to spend a couple hundred on this part/installation.
Are there any known workarounds? If I can get the latch to secure tightly enough, I can just open the main liftgate from now on, instead of just the glass portion.
Thanks in advance