What is the hook to remove a menu items group from Appearance > Menus column Add menu items

You can use the register_post_type_args filter and just set the show_in_nav_menus argument to false. E.g.

add_filter( 'register_post_type_args', 'my_register_post_type_args', 10, 2 );
function my_register_post_type_args( $args, $post_type ) {
    if ( 'post' === $post_type ) {
    // or use below to check against two or more post types
//  if ( in_array( $post_type, array( 'post', 'cpt_1', 'cpt_2', 'etc' ) ) ) {
        $args['show_in_nav_menus'] = false;
    }

    return $args;
}

And just so you know, for taxonomies (category, post_tag and custom taxonomies), you would use the register_taxonomy_args filter.