What does "wipe your chin and walk away" mean?
Solution 1:
There are two possible meanings for the phrase. The basic concept is that you've been wronged but you're supposed to be thankful for the chance to be wronged by the person.
The more likely candidate is that you are on the giving end of male oral sex but supposed to be thankful for it. See for instance here: http://www.screenit.com/movies/2010/the_social_network.html
The less likely candidate is that they punch you in the lip, so your lip is bleeding, but you are supposed to thank them for that. I can't find any support for this interpretation.