In the short story "The Necklace" by Guy de Maupassant, Monsieur Loisel indeed tells his wife Mathilde to write a note to the latter's friend and tell what we could consider a "white lie" to save his wife's reputation.
"You must write to your friend", he said, "that you have broken the clasp of her necklace and that you are having it repaired. That will give us time to turn around".
She wrote as he dictated.
From that statement you can make the assumption that a letter was sent, regardless of whether or not there is any consequence from it. There is no point of having those lines included unless it is going to be done. Moreover, the fact that Madame Forrester was merely "irritated" by the delay in returning the necklace hints that the fact that she already knew that the necklace will be returned late, just not as late as it took for Madame Loisel to return it.