I'm not quite sure what Hermes' goal was with the letter either, if he made it.
The letter was described as being indecipherable, save for a sentence at the bottom, the rest was just scribbles and unreadable as described by the flavour text. "I'm sorry for not being good enough. .P" is specifically what it says. After you read out the letter, Hermes says Clement was the name mentioned by Headquarters.
Hermes said it was from headquarters, and, since he is an Olympian, I would interpret that as the letter being from Poseidon, who in the story is technically Asterion's father/grandfather. He voted in favour of Asterion, but we have no transcript of it yet, that content isn't in the game currently.
The only other Ps we know of are Pedro, and Pedro's father.
As for it being a ploy to get Asterion and MC even more intimately involved, I don't think that is the case. Why would Hermes interrupt the happiness by making Asterion distressed? Just so MC can emotionally support them? Perhaps it is some kind of test? But letting Asterion know that Clement is still alive seems more like some form of torture than anything else. Hermes is clearly in Asterion's side of the ring, too. However, he did succeed in making MC and Asterion talk more about their feelings. But it could equally just be Olympus making sure Asterion suffers a little more.
It's tricky, with what little information we have. Poseidon may be a stretch, but we are limited on choices regardless. I feel that the story of Clement may be somewhat related to Tithonus, a man who was given eternal life, but not eternal youth, and went mad as his body refused to die. The main takeaway from that story was that Asterion ended the man's life with the Threadcutter labrys, a weapon which can kill the immortal, and that "to free somebody from their shackles, you take on your own". This is also shown in the Ruthless ending where Asterion leaves the hotel, and only Argos stays behind, his pelt turning him into the new minotaur.
Perhaps we simply don't have the information required to solve this mystery yet? Or maybe it is as simple as Hermes screwing with us for fun?