I assume your directory is a userlist? If it's a userlist you should be able to just add a filter to that userlist against your field to filter those users out.
If not, is there any point in having this option since the only way to not have the contact info displayed would be to remove the user profile altogether?
I've no idea. I didn't make that website so I can't know the intent of adding that. Ideally you'd just use CB Privacy to let users control field visibility themselves.