duplodon Devora really said it all already, but letterbox is supposed to be for the children. Think about how an 8 year old, for instance, would feel if they were given that to read. It would likely be confusing, very upsetting, worrying, potentially led to the child feeling personally responsible for their birth mother's sadness, and personally responsible for fixing her sadness themselves, maybe guilty for loving their adoptive family or feeling happiness in their family life. I can't see it leading to anything other than very negative emotions in the children.
It's not a problem and completely natural that their birth mum is crying and missing them deeply. It's about how you express it and to whom - in effect guilt tripping a young child and putting pressure on them to come and find you to fix your sadness asap is not beneficial for the child, it's going to be emotionally harmful to them.
Very sadly it demonstrates that birth mum isn't able to put herself in the childrens shoes, think about what they might need to hear and put them before herself. That's not uncommon, but absolutely it's very sad. So the onus is on the letterbox coordinator to do their job properly.
I've done letterbox for a long time. It's usually difficult and very emotional for absolutely everybody, but the key is that everyone has to put the kids feelings first. I put so much thought into my outgoing letters, and I never expected their birth mum to be able to just fire a letter out or not find it incredibly difficult to write, and I didn't expect her to manage to write all the letters without anything inappropriate in them - but I DID expect social services to monitor letters and not pass on anything like MissF's letter.
MissFenella, I would absolutely send it back with a letter basically saying you can't accept anything which is going to be emotionally harmful for your DC's, and you hope it can be reworded.