Get the parent items of a menu item
There is not an easy way to get the parent of a specific menu item. The problem is that a path can be in many menus so you need to not only know the path of the item whose parant you want to find, but also which menu to look for them.

The menu_links table hold the info and with a few queries you could find info about the parent. If you actually want to change anything in the menu being printed, that's a completely different story, and can be quite tricky in Drupal 6.

To get menu item you could do something like this:

$path = 'foo';
$menu = 'bar'
$mlid = db_result(db_query("SELECT plid FROM {menu_links}
          WHERE link_path = '%s'
          AND menu_name = '%s'";, array($path, $menu)));

$menu_item = menu_get_item($mlid);
// $menu_item is now the parent menu_item of the menu in bar with path foo