A letter from Curley is going to highlight the "surface" approach he takes towards living.
Curley is a "surface" character. He lacks the depth of Slim and lacks the understanding of someone like Candy. He is the boss's son and enjoys the privileges that go with it. As a result, much of what he would write would focus on what he immediately perceives. The letter would lack much in way of emotional depth because this is something that Curley himself lacks.
A letter could focus on how Curley is distrustful of the new arrivals.His letter could address how George gave evasive answers in their first encounter. Curley could not understand why George and Lennie travel around together, evident when he remarks "So, it's like that, huh?" George held his own against Curley, and refused to capitulate to begging and deferential respect. Curley might write about how he saw this as a direct threat. Given how Curley does not like "big guys," his letter might also spend some time discussing how Lennie is someone towards whom he must be vigilant. Curley could mention that Lennie did not speak when addressed. While he doesn't indicate this in the text, it is clear that Curley understands that something isn't quite right with Lennie. He could allude to this in his letter.