does teamviewer start any webserver on a local port which the banking page could connect to and check a _running_ instance? Would be much more interesting for fraud detection than a _installed_ instance
you can't query local services from a remote webpage unless you use a dns rebinding attack which is probably a bit over the top for "whitehat" activity.
but only because the local service in this example is not prepared to accept the websocket connection, the teamviewer client would be able to do this to enable some functions on the teamviewer website if a instance is running