I got in the habit on SO of removing thanks and signature lines (and greetings) during edits because they don't add to the question and are relatively unneeded. I think we should adopt the same policy here and remove them from questions where they appear (and ideally not include them when writing new questions).
I don't mind going through and editing questions to remove them, but I would like it to be something everybody does so when they re-tag or edit questions for other reasons, they can remove these lines too.
You can find questions of this sort by searching:
thanks closed:no is:question
where you can replace thanks with whatever other words that could bring up things like greetings and signatures.
For the record, here is the MSO discussion on the same topic: