The z-index controls what elements is shown above others. So the header and the parts not covered by the pop up are behind it because the z-index for those is higher. Now, with the header not being stuck behind grey, I personally would not mind, it keeps users still “on the site” and not “like in a dark room somewhere else”
I have some problem with my computer right now and can’t open files properly, so I can’t take a look if the module has an own css, what it should have. So basically you have to find a css inside the directory and in this css somewhere you should find “z-index” and a number following it in a row that must be called somehow like “#catpopup pop up”. You can set this to 10000 for example, this should be high enough to set the grey covering above all. When the header is still above it, try setting it even higher than 10000.
When all this does not work out, maybe someone else can help.