MS Paint keeps a list of recent used files in the registry.
If you only want to clear the recent file list in MS Paint and you are comfortable editing the registry, delete the key: HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Applets\Paint\Recent File List
Or use attached txt file. (rename to NoMRUPaint.reg)
Close MS Paint and doubleclick NoMRUPaint.reg to import into the registry.
Your recent file list will be empty again.