Change Order Note

I would like to change the order note on the view order page when a new order is created but only when the payment method is cash on delivery. The code below can change the order note but I can’t figure out how to do it only for cash on delivery. If not cash on delivery then the normal order note should still appear.

add_action( 'woocommerce_new_order', 'add_engraving_notes' );
function add_engraving_notes( $order_id ) {
	//note this line is different
	//because I already have the ID from the hook I am using.
	$order = wc_get_order( $order_id );

	// The text for the note
	$note = 'No special message yet';

	// Add the note
	$order->add_order_note( $note );

	// Save the data
	$order->save();
}