Dieter,
My experience: it is always good to look at Tech Manual
. Lot's of info on forum too.
As the door is riveted to the rest of the glovebox with two rivets, you need to remove the whole glove box and then unscrew the door or travel to France with the whole glovebox using it as e.g. lunchbox.
To remove the glovebox: mask the dash and leather around with the painters tape not to scratch anything (do not leave the tape stuck to car - it may leave marks), unscrew, I think, 6 screws (4 bottom, 2 top) and probably the switch. Then depending on how long wire you have for the lamp - either you can remove the glovebox and then disconnect the wire inside the dash (I did not try to undo the lamp, and it may be easier way) or dive under dash to disconnect it.
Once you have the box out, you would need to disconnect the forks and spring and unscrew the 4 screws that hold the door to the hinge.
Alternative: dive under dash, disconnect the cable (or undo the lamp - I have not tried this, was afraid to scratch the paint on the outside of the door), disconnect the forks and springs, unscrew the 4 screws that hold the door to the hinge and while removing door, find your way out for the closing bent rod through the oval rosette out.
I think the first way is the proper way, actually...
On re-assembly I would be careful when tightening the 4 screws that hold the door to the hinge - on some other part -when I did it too tight the paint cracked and came off. Since then I put a bit of some lubricant under the screw head in similar situations, but I do not know if it is a good practice.
I think you would need to adjust the door - but then the holes in the hinge are much larger than screws diameter, which gives you some play to set the door. Be careful not to scratch the dash and leather around when adjusting/installing- use painters tape to mask them again. Or some thick static foil maybe.
I have not experienced adjustment issues if the box was once fit in its place... but maybe others have.