You have an access issue with one of your control files so you need to examine the project structure in the Windows Explorer. This has nothing to do with adding (or removing) a class to a project. The general structure for C++/MFC projects is:
<PROJ>.vcxproj // the main project control file, used to build the project(s)
<PROJ>.vcxproj.filters // the control that groups files into folders in the project.
<PROJ>.vcxproj.user // not sure what this one is for, but if you delete it, VS will recreate it.
where "<proj>" is the name of your project.