When you use jump points to enter a system, you get a warning that your transponder is off, and an option to turn it on before jumping.
With the Transverse Jump ability, there is no such warning and you can jump straight into a bunch of sector fleets with your transponder off. There should be something that at least lets us know about it.
I don't like the intrusive jump point screen interface, so I'd suggest a flashing message that says something along the lines of "Warning: Transponder offline", while the ship is warming up for a jump. That way I can ignore it if I want the transponder off, but I also won't forget that it's off.