wp_nav_menu_items for one menu

I came across your question by looking for an answer myself. Here is how I made the code work for me:

function new_nav_menu_items( $items, $args ) {
    if ( $args->menu == 'primary' ) {
        $items = "";
        $args = array(
            "post_type" => "page", 
            "order"     => "ASC", 
            "orderby"   => "menu_order"
        );
        $the_query = new WP_Query( $args );
        if ( $the_query->have_posts() ):
            while( $the_query->have_posts() ): 
                $the_query->the_post();
                $items .= '<li><a href="#post-' . get_the_ID() . '">' . 
                    get_the_title() . '</a></li>';
            endwhile;
        else:
            echo "";
        endif;
    } 
    return $items; 
}
add_filter( "wp_nav_menu_items", "new_nav_menu_items" );