I am not sure writing a letter H is a good idea...even a short paragraph. Obviously if writing the letter is a cathartic release for Claire, then she can do it and BURN it. Or never sending it.
For me, I've written several letters to Ms. Wonka and never sent them. Except for one pre-DB that was pleading, begging, and whatnot. Chalk that one up as pure ignorance on my part. Ever since, I've written forgiveness letters to Ms. Wonka and did not ever send them.
It might be helpful to Claire to write them and get her feelings out of the system. Then don't send any of it to H.
Gosh, I strongly encourage Claire NOT to send any letter(s) to H.