I came across this thread as a top result in a web search, but unfortunately the given answers didn't work for me. I did some thinking and figured that whatever Windows Process is responsible for Drawing graphics/windows onto the display would need to be restarted. Turns out, all you need to do is go to process manager (ctrl+shift+esc), find "dwm.exe" (under details display) or "Desktop Windows Manager" (under processes display, subsection "Windows processes"), and choose to End Task. No, there is no "Restart" option, but Windows will automatically restart this process once it is killed, so it's effectively a Restart action.
Why is this a fix different from the previous responses? If a window closes without properly telling DWM to remove all of its GUI from the display, the action of restarting DWM will remove it. Because, of course, the application that was responsible for drawing it is not running. So you can't re-kill a dead process. It's just that DWM just didn't get the correct message that the app was closed and thus DWM didn't take the action to remove it. It logically follows, if you get DWM to restart cleanly, it would not attempt to draw a non-running process.
For the sake of boosting more web-search foo, this is what I ended up searching DuckDuckGo with to find this thread: "i closed a windows application but the program bar is still on screen what process do I restart to clear that"
