The idea is to present a quick-access method for folks to come to your site and remove themselves from your newsletters if they no longer wish to receive them. As such, the link shows to everyone, whether logged in or not.
If you do not wish to display it, turn it off:
Admin->Configuration->Email Options->Display "Newsletter Unsubscribe" Link?
By the way, have you ordered your copy of the
e-Start Your Web Store With Zen Cart book? It's a comprehensive user/administrator manual that deals with this sort of topic and more.
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