How do I remove these escutcheons from my door?
All GU hardware I have installed, the plate is a pressure fit in place, the notches you see are for removal. The thumbturn in many cases, but maybe not this one, has been in the past, a one piece unit with the cylinder. The torx head screw on the edge is about 3" long and is threaded into the cylinder, usually.

The picture with its angle does not show the bottom half of what may be the cylinder that the thumbturn is a part of. A picture of the outside of the door may reveal the key slot, so I would assume.  Never the less, if it is put together like all the others I have worked on, removing the torx (star)screw will allow the cylinder to be removed from the thumbturn side and after the handles are removed the escutcheon can be gently pried off by working the top a little, then the bottom, and so on until it comes free. 

If you have a putty knife to hold at the top edge while the screwdriver is rotating to start prying the cover plate off, it will prevent any damage to the nice finish you have on the door. o the same with the bottom slot too.