The headlight door on each side of the car is held in place by two Philips-head screws situated in the gaps between the two lamp openings, making them easy to extract.
Here's the left door as it was removed from my car. Both are probably the original Bosch-made units:
Here's a view of the back of the door:
The backsides of the doors have small plates of zinc in them, for the purpose of reflecting ambient headlight output throughout the door. Over time, the zinc gets dirt-fouled and corrodes.