Elles se sont écrit des reproches, mais leur relation reste solide.

Questions & Answers about Elles se sont écrit des reproches, mais leur relation reste solide.

Since the subject is Elles, why isn't there an -es at the end of écrit?
With reflexive verbs in the passé composé, the past participle usually agrees with the subject. However, there is an exception: if the reflexive pronoun (se) acts as an indirect object, there is no agreement. Because you write to someone (écrire à), the se here is indirect, so écrit remains unchanged.
Since des reproches is the direct object here, shouldn't écrit agree with it?
Only if the direct object comes before the verb! In this sentence, des reproches comes after the verb écrit, so no agreement is made. If the sentence were rearranged to put the direct object first, such as the reproaches that they wrote to each other (les reproches qu'elles se sont écrits), then you would add an -s.
How can I easily tell if the reflexive pronoun is a direct or indirect object?
A great trick is to rephrase the verb in your head without the reflexive pronoun to see if it needs the preposition à. Because you say écrire à quelqu'un, the pronoun replacing that person is indirect. If the verb takes no preposition, like with laver quelqu'un, the pronoun is direct and the past participle would agree.
Why is it leur relation in the singular when Elles refers to multiple people?
Even though Elles refers to multiple people, they share one single relationship between them. In French, when multiple possessors share one single item or concept, you use the singular possessive adjective leur followed by a singular noun.

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