Does telling relatives and friends about a cousin's attempts to attract her fiancé's attention, which led to the annulment of the engagement, constitute backbiting (gheebah) and harm to her, and how can one repent from that?

If the cousin (daughter of the maternal aunt) is mentioned in a negative light for a valid reason—such as seeking advice or help in changing a wrong (munkar)—then there is no harm, provided that the wrong is verified, because backbiting is permissible in such situations.

However, if the mention is not for a valid reason, then it is forbidden backbiting, and one must repent from it by ceasing the act, regretting it, and resolving never to return to it. Part of repentance is seeking forgiveness from the cousin and mentioning her positively to those before whom she was mentioned negatively.

If seeking her forgiveness would lead to a greater harm, then repentance and mentioning her positively to those before whom you backbiting her will suffice.