The famous pilot scenes where Scully goes to Mulder in her underwear to have him check out her bug bites and the conversation that follows are truly great moments of television.
Here you have this scene that is arguably not Scully's best moment. Or that's probably what you'd think if you were in her shoes. You'd probably be embarrassed that 1) you believed that you could have alien spots on your body 2) when they were in fact mosquito bites and that 3) in your absolute panic, you showed up to your new partner's room in your underwear for him to check it out.
But Mulder is the perfect gentleman as it happens. No joke, no innuendos, and even no compliment (even a compliment could be weird in this context). Nothing except "Oh yeah, I got mosquito bites too."
He even opens up to her in response and shows some vulnerability himself. Here is he, spilling the beans to an agent who may or may not have been sent to debunk his work.
And Mulder never throws that event back into her face (canonically), whether as some kind of argument, or even as a joke or a tease ("you showed up to my hotel room in your underwear on OUR FIRST case" ). You also don't get the impression that he's told the Lone Gunmen, or anyone else for that matter. He's taking that moment to the grave.
And, as for Scully, she's able to see that Mulder isn't just some guy who pursues the cases he does for fun, that Mulder is serious about what he does.
It is a fantastic show of trust from both of them. And I like to believe that Scully probably looks back at that evening... maybe not fondly, but she doesn't cringe about it.