How to remove the lower glove box door ?

You push in the sides, you'll see tabs on each side. And the shock just pulls off on the door.
Then just pull it out where it hinges.... If you look at it closely, you'll see how it's attached.
No tools needed.

 

Edit to add -- Oops! You have a Gen 3. No problem. It works the same way.

 

What I do (as best I can recall):

1. Empty everything out of it.
2. With the lid open, grasp near the ends and pull it up and off the hinges.
3. Reach around the right side and disconnect the little piston damper.
4. Press the end walls together, wiggle-waggle the whole thing, and pull it towards you. You need to get the whole thing free of the end wall retainer tangs, and those actions seem to do the trick.

Putting it back in, I'll usually start by holding it in open position, and get it pushed back onto the hinges. That can be easier said than done; it can help to get on your back on the floor, looking up. Once it's on both hinges, reconnect the damper, then slowly close it, and as you do the end wall retainer tangs should pop back into place.

Finally just open and close it, make sure it moves normally, everything uniform.