What should be done about an anonymous letter accusing a married couple of openly flaunting their sexual desires and of debauchery, describing the husband as a cuckold and the wife as a harlot, especially given that the wife fears people's talk and is concerned about her reputation?

What the person did by writing this obscene message is a reprehensible evil act. The best solution is to completely ignore the matter and not search for the perpetrator, for in that alone its harm will be repelled. Do not tell anyone about this incident. As long as you are among those who are obedient and preserve the limits of Allah, this will not harm you, Allah willing.