No PuTTY tool will ‘phone home’ to any site under the control of us (the development team), or to any other site apart from the destination host or proxy host in its configuration, and any DNS server that is needed to look up the IP addresses corresponding to those host names.
No information about your network sessions, and no information from the computer you run PuTTY on, is collected or recorded by the PuTTY developers.
Information you provide to PuTTY (via keyboard input, the command line, or files loaded by the file transfer tools) is sent to the server that PuTTY's configuration tells it to connect to. It is not sent anywhere else.