You guys are assuming that he wrote a love letter to her, when given his already demonstrated denseness and upstanding behavior, his letter was most certainly just a very professional "thank you" where he acts more or less like a school teacher giving advice and praise to a star student in their class in response to said student taking a great effort to demonstrate how much they respect and admire the teacher for what they've done to them.
Oh sure, she would see it as little to no different from an actual love letter, but most people wouldn't bat an eye.