First, close Outlook, and then open up the Task Manager, by
right-clicking on the Windows Taskbar and choosing Task Manager.
Next, check the processes list, and verify that Outlook
(outlook.exe) is not running or listed in the processes list. These
initial steps are to help us determine if the problem is with the
Outlook application not closing properly, or some other component
in the system.
If Outlook is completely closed, and the remnants of a search window are still there, try right-clicking on the desktop and choosing the refresh option to see if that tidies things up. However, that's only a work around. I think the solution in the end will involve updating your video card driver. The video card is the component that is responsible for properly refreshing screen elements. If the card is overheating, or in the process of failing you can get some flaky performance. However, something like you've described here could be fixed just by updating the video card's driver. Good luck!