I had exactly the same problem about six months after I purchased my 2002 E300. Here are the instructions I wrote to myself and I use them every time I change the filter. Hope it works for you.
REPLACING THE CABIN AIR CONDITIONER FILTER
- Remove Phillips head screw from right side of glove compartment door and pull the lifter mechanism away from the post.
- Reach in to compartment and turn the plastic turn buttons a quarter turn to the left for the left hand button, to the right on the right hand button, and pull the buttons in to the glove compartment.
- Lower drawer and pull toward you
- Grasping by outer edges, pull the compartment containing the filter toward you.
- Install new filter, make sure the arrow stamped on one side of the Toyota filter points up.
- Replace filter drawer and tape or wire right side shut.
- With the glove compartment tilted well down toward the floor, engage the hinges so that the bar on the dashboard is BETWEEN the two prongs on each hinge.
- Reinsert the plastic button on each side of the compartment. Note: the buttons only go in one way, if they won’t turn once in rotate them 180 degrees and try again.
- Reattach lifter mechanism and reinstall Phillips head screw.
- Record on service record.