Should I agree to teach a class for my supervisor even though I don't get any acknowledgement for it?

This already has too many answers, but I can't help myself: academia entirely runs on people doing stuff they are not contractually obligated to do. This generates a lot of problems along the way, but that is how things stand. "It's not a formal requirement that I do this" is not likely to be a satisfying answer for your supervisor. If the amount of lecturing is not a huge burden, and you feel like it will not make a huge dent in your productivity, then it is probably a worthwhile thing to do (if only as a favor to your supervisor); if you feel like the amount asked is a large burden, see if you can negotiate to reduce it. I also agree that you want to get something in writing. I would phrase it as "I want to be sure I understand what needs to be done for the class. If it's writing, it's less likely I'll forget or misunderstand," rather than making it seem like you are suspicious.