No, there is not an option to hide the menu entry to anonymous users, just a method to keep anonymous users out (Login Required setting).
If you want to manually remove the entry, you can edit the Media Gallery functions.inc file (plugins/mediagallery/ directory).
Text Formatted Code
function plugin_getmenuitems_mediagallery() {
global $_CONF, $_USER, $_MG_CONF;
$menulabel = $_MG_CONF['menulabel'];
$menurul = $_MG_CONF['site_url'] . "/index.php"; // Menu url here
$menuitems = array();
$menuitems["$menulabel"] = $menurul;
return $menuitems;
}
Text Formatted Code
function plugin_getmenuitems_mediagallery() {
global $_CONF, $_USER, $_MG_CONF;
if ( !isset($_USER['uid']) || $_USER['uid'] < 2 ) {
return;
}
$menulabel = $_MG_CONF['menulabel'];
$menurul = $_MG_CONF['site_url'] . "/index.php"; // Menu url here
$menuitems = array();
$menuitems["$menulabel"] = $menurul;
return $menuitems;
}
This change will now only show the menu entry to users who are logged into the site.