The Telnet proxy used TCP keep-alives on the connection to the client. The Telnet proxy insists on doing its own echoing during the initial user authentication portion of the session. Some Telnet client programs do not obey standard Telnet echo negotiation and improperly double-echo username/hostname input and single-echo the password.
By configuring the Telnet proxy on a Screen, the actual Telnet service into that system becomes unavailable. To avoid confusion, define the destination address of proxy rules so as to exclude all of your Screen(s) addresses. (You can still use the rlogin protocol to access the Screen, as necessary, as well as being able to telnet out.)