The speaker writes letters, but not to a person. The addressee is "some other sea," which is strange enough, and the poem makes it stranger by describing this sea as someone who "lay long in bed" and who was "formerly and now again / to be employed as the sea." It reads as if the sea is a worker who has been idle and is about to be put back on the job. That odd, almost bureaucratic image sits against something as vast and natural as an ocean.
The final line gives the letters their purpose: they are about "the admiral, an old hypocrite." The title, "Poison Pen," fits, since a poison-pen letter is a spiteful, accusing one. The speaker seems to hold a grudge against a figure of naval authority and chooses an unusual confidant, another sea.
The mood is dry, playful and a little bitter. The poem never explains itself, so the humor and the resentment both come from its deadpan tone.