If anyone is still looking for this in 2020 like I was, don’t try prying anything or poking around with those tools or you’re likely to break off some plastic tabs that you don’t want to break off while not accomplishing anything useful.
The gray plastic cover is attached to the metal cover by two tabs go under the metal cover. The location of these tabs is on each side of “amazonkindle” logo on the metal cover. Simply put your thumbs on each side of the logo to get them in the correct position, then slide them over to the plastic piece so that they are near the tabs (which you cannot see), and then press down gently to disengage the tabs while pushing the gray plastic piece away from the metal piece. If you do it right, it slides off easily.