After you set up PuTTY's configuration for a particular network connection, you can choose to save it as a ‘saved session’, so that you can make the same connection again later without having to re-enter all the details.
PuTTY will not do this unless you use the ‘Save’ button in its configuration box. It never saves session configuration automatically.
So if you want to make an SSH connection without leaving any trace of where you connected to, you should not make a saved session for that connection. Instead, re-enter the details by hand every time you do it.