Politeness is important in human-human interaction when asking people to engage in sensitive conversations. If politeness manifests similarly in human-chatbot interaction, it may play an important role in the design of sensitive chatbot interactions such as those for providing mental health support. Our mixed methods study (N = 39) contributes findings on how the use of politeness by chatbots, for the mental healthcare activity of mood logging, is perceived by users. Our study combined a within-participants controlled experiment, whereby participants interacted with three prototype chatbots differing in their use of politeness, with semi-structured interviews. Our analysis demonstrates that a chatbot’s use of politeness can impact how a participant experiences interacting with it, both positively and negatively. While politeness can be experienced as caring, supportive, and encouraging, it can also be experienced as overly apologetic, condescending, and untrustworthy. We discuss the nuances of using politeness in conversational interaction design, setting out a research agenda for polite conversational interaction.