I believe that you'll find the tank badges to be die cast metal parts, not plastic. It's fairly flexible when removed and pretty easy to bend or distort if you're not careful. That being said, it's also reasonably easy to gently bend it back into shape unless you bend it too sharply when removing (see below).
As noted, there are two posts on the back of the badge that press into matching holes in the tank. There are also little metal clips in these holes that help the posts snap into place and hold retention.
I've found that the best way to remove the badges is to pry them off with a thin plastic tool. The kind of tools that you can find in auto parts stores for removing interior trim or radio face plates are good for this purpose. Like these:
http://www.ebay.com/itm/Car-Door-Plastic-Trim-Panel-Dash-Stereo-Audio-Radio-Installer-Removal-Pry-Tools-/201258227428?hash=item2edbecd6e4&item=201258227428&vxp=mtrDon't start prying the badge off at the very end; start about an inch in from the end. That's approximately where the mounting posts are. If you start lifting the at the end, you may put a sharp bend in the badge right where the post is. Experience talking. Lift it a bit at a time and place a shim of some sort under the badge as you pry one end up a little bit, then the other. It should come off without much struggle (unless some previous owner has used the double stick tape method to put it on).
When you put the badges back on, you'll want to make sure they are
not perfectly flat. You want to have a slight curve in the badge to match the curvature of the tank where they mount. Make sure the little metal clips are in place in the tank holes, then press the badges back on.
