You see, the letter she wrote could be understood in both ways. It was a neutral message. And Rudeus, being a virgin shut-in neet in his previous life, understood that the fault was on him.
Here, it's the opposite, Sara, that bitch, intentionally lied to make herself feel better at the cost Rudeus. There's only one way to interpret what she said. That she wasn't interested in him and was only doing it, because he saved her. Like a favor of sorts.