Smash Party by default does not store chat messages sent between users and switches. However, if someone creates a room and enables "Save Chat History", then chat messages will be saved on the server. Check with the room creator whether Chat History is saved or not before sending any message (you shouldn't be sending any personally identifying nor any sensitive info here anyway.)
If you understand that your messages may be potentially saved depending on the options the room creator enabled, press the "I understand" button.
