If you hover your mouse over the project, it should say something like "Project Not Found." For any project with that status, clicking on it will prompt you to remove the shortcut from the list. There is also an XML config file you could modify if you are so inclined, but I am guessing discourages it since I haven't seen them mention editing the file in any of their documentation.
This issue was brought up during beta testing of ArcGIS Pro 1.0. Several users were interested in having the list only include projects that were accessible/found. Off the top, I can't remember what Esri's response was, but obviously they either think the current functionality is ideal or they just haven't found time to fix it yet.
