I don't think there's a formal policy, but I'll talk about what I've noticed myself doing.
If someone just says 'thanks', I tend to leave it, even when doing a lengthy edit, even though it strictly doesn't belong.
However, if I'm removing a subsequent signature, I may take 'thanks' as well.
If it's a long rambling thanks (say a couple of sentences) I take it out.
I object to the distraction of put-downs of the question or apologies for asking a basic question by the asker and tend to have a strong impulse remove those or encourage the OP to. (Not least because it puts down other users of the site with the same problem. They may think they're only calling themselves dense or uneducated, but since the questions are permanent, and often posted questions are questions other people have, ... they aren't)
There's potentially a similar put-down with the basic-concepts tag. I'd say easily 2/3 of the posts with the tag don't come remotely close to being basic (people tend to underestimate the non-basicness of their problems, sometimes drastically), and many of the ones that could rate such a tag ... well, I often wish they wouldn't, for the same reason I don't like "sorry this is such a dumb question".
We were all ignorant once - what's so wrong with a basic question that we must apologize for it? I don't come here only to answer questions at the outer edge of my knowledge. Indeed, sometimes formulating a good answer to what looks like a relatively simple question can be a surprisingly subtle task, and the review of the basics from a variety of viewpoints can often be helpful even when it's reasonably familiar territory.
Of the emotive statements that come up, the kind that tend to get me the most is begging. I find those particularly objectionable. (I don't so much object to a simple factual statement about time pressure, but multiple lines of "PLZ answer my question" or even worse, a title with it... that stuff pushes my buttons for several reasons at once.