By default WooCommerce order notes are not showed in the invoice.

If you want include them please add following code to the file functions.php of your theme.

if ( ! function_exists( 'yith_ywpi_show_order_note' ) ) {
    function yith_ywpi_show_order_note( $document ) {
        $order_id    = $document->order->get_id();
        $order_notes = wc_get_order_notes( array( 'order_id' => $order_id ) );

        if ( ! empty( $order_notes ) ) {
            echo '<b>Order note</b><br>';

            foreach ( $order_notes as $order_note ) {
                echo wp_kses_post( $order_note->content . '<br>' );
            }
        }
    }

    add_action( 'yith_ywpi_template_order_content', 'yith_ywpi_show_order_note' );
}

The code take all order notes added to the order manually or automatically by the system .