I don't think there is such thing for Messenger. I have the latest version installed and didn't notice any conversation leaks over the Internet for my chats, even if they're public or private.
Try updating to the latest version because it's secure and safe to use it, however, always install the latest version from the Play Store application in your phone. If you insist on staying secure, install Malwarebytes Anti-Malware and scan your phone, then remove it.