Since all users, whether authenticated or not, can see guest content, you can't use permissions for that. It is also somewhat wrong since the guest content isn't actually secret for authenticated users.
I am not sure, what you need to do exactly, but in general you need to add a check to the component to hide it if the current user is not the guest user. If it is really a navigation menu, you could write a template to do that. We also often just do things like that using css. Hide or show things based on some logic.