@tmeks solved this problem as follows. This only affects the Engine once launched (open project) it does not change the list that show in your library.
Open the file at:
%localappdata%\UnrealEngine\4.9\Saved\Config\Windows\EditorSettings.ini
You’ll see some entries like this:
RecentlyOpenedProjectFiles=C:/Users/[YourUserName]/Documents/Unreal
``Projects/MyProject/MyProject.uproject
Just remove the line with the path to the project you don’t want to show up, save and restart the UE4 Launcher. That project should no longer appear under “My Projects”. (Until you open it again)
(You probably want to replace 4.9 in the path above with the most recent version number)