I've had this issue since last year, and have exited the program / rebooted my computer many times during this period. I can't remember when it started, I mostly just ignored and worked around it. I've worked out it only happens in certain circumstances.
To replicate the issue:
1. Have Evernote windowed
2. Click to annotate, the annotate window is fine.
3. Go full screen. As it goes full screen it's like that part of the window (the border around the edge) just doesn't go with it and I get left with what I call the ghost window, which I guess is just an element of the window not performing correctly. (Does that make sense? I could make a video?)
If EN is full screen, and annotation opens in straight into fullscreen, I don't have this problem.
Now that I've worked out I can avoid this issue by making sure EN is full screen whenever I go to annotate in fullscreen, I'm not too bothered by it. Just figured someone ought to know that there's a lil bug