Anyone who can help a 'Newbie'?

I am using the 'Echo Both' example code for serial testing on the Teensy 3.5 board, with a USB to serial convertor lead from another computer which has RX, TX and ground connected to RX1, TX1 and GND on the Teensy board.
I am using 'RealTerm' on the computer to send data to the Teensy serial port via the USB-Serial convertor lead.
I have checked that data is being sent correctly from the computer by monitoring it using 'RealTerm' on another computer, and data is being sent and received correctly. Baud rates are set at 38400.
Using the Arduino serial monitor, I get the expected result when sending 'A' via the USB serial connected to the Teensy board i.e. the monitor shows:

USB received 65
USB received 13
USB received 10

But the 'RealTerm' monitor just shows garbage:

UVTʪjTZ6VVU۪ʪjTZ֖VoU۪ʪjTZVo 

with the occasional brief showing of 'UART Receiver Framing Error' in the bottom status bar. I have triple-checked the baud rate, parity and stop bit settings.

I get no response in the Arduino serial monitor when sending from the other computer using the USB-Serial convertor lead, but some activity (UART received) is displayed if I connect and disconnect the serial connections (RX and TX) to the Teensy breadboard.

I would be very, very grateful of any help that anyone can give,

Many thanks,

Allen