drupal 7 parent menu item will not hide for authenticated user
The easiest way with the least amount of programming would be do it with css: 

body.logged-in .my-menu-name-or-css-class {
  display:none; 
}


The most standards compliant way would be to use hook_menu_alter and unset the menu if $user->uid returns true: https://api.drupal.org/api/drupal/modules%21system%21system.api.php/function/hook_menu_alter/7

However, in this case you're probably looking at maybe saving 10kb of bandwidth by unsetting the menu vs. just using CSS to hide it.