WooCommerce: display text instead of raw checkbox value email

Try this instead:

add_action( "woocommerce_email_after_order_table", "my_woocommerce_email_after_order_table", 10, 1);

function my_woocommerce_email_after_order_table( $order ) {
    $my_gift_wrap_checkbox = get_post_meta( $order->id, "my_gift_wrap_checkbox", true );
    $gift_wrap = $my_gift_wrap_checkbox ? 'Yes please!' : 'No thank you.';

    echo '<p><strong>Gift wrap?: </strong>' . $gift_wrap . '</p>';

    if ( $my_gift_wrap_checkbox ) {
        echo '<p><strong>Gift wrap instructions: </strong>' . get_post_meta( $order->id, "my_gift_wrap_field", true ) . '</p>';
    }

}