The portion that exposes the drink holder pulls straight up after two tabs are pushed in. Access these tabs by opening the armrest. Then, while pulling gently upward push in one tab with a screw driver then pull upward on the other side while doing the same. It will pull straight upward.
The portion of the armrest closest to the driver can be taken off by removing the two (1 each side) T-10 fasteners. You can get to these by opening the armrest to the compartment that holds the phone.
This one didn't have any screws. I found a video on YouTube after posting this and it shows that they glued the top on. Glad I didn't attempt to remove it the car was 18 years old and plastic was already brittle in it. This industry gets scarier every time I turn around.