Can't find bypass on aftermarket remote start

Hello all, I've searched the web and this site in particular and I'm having no luck (said almost every new member on their first post). I had an aftermarket remote start installed on my wife's 2013 Tucson. There was a charge to add the capability to bypass the immobilizer, but I can't recall if it was an upgrade to the remote start, or if they told me there was a separate module. Anyway, the car is a lease and it's time to turn it in. I removed the remote start by tracing all of the wires to where they're spliced into the car's wiring, but I found no separate module. There was only the Directed 4x03 (I think it's marketed as Avital 4103), the antenna, and a relay connected to the ignition harness. Nothing was wired to the OBD interface either. Is it possible that this kit is able to bypass the immobilizer using the relay, or is there a bypass module that I'm not seeing? I would imagine that if there was a bypass, it would have to be wired to the remote start module, but please let me know if I'm wrong. My ultimate goal right now is to ensure there isn't a module installed that I'm going to wind up leaving in the car when I return it. Thanks in advance!

In case more information is needed: 2013 Hyundai Tucson GLS AWD Automatic US

I've never seen a U.S. car with transponder. It would be fun if you could find the receipt for the system then challenge them on the charge for installing something that wasn't needed and not in the car.

I'm pretty certain I've had one in every 99-02 GM I've owned, but I think your response has helped me find the answer I need. Hyundai doesn't even sell an immobilizer for the 12-14 Tucson models, and I can't find anything in those years stating there is an immobilizer feature. Too bad this is from 3 years ago and my wife tossed the receipt. Thanks for the input. I am still curious, I'm sure I would have seen the remote start unit wired to a bypass if there was one, right?

Oh, I meant U.S. Hyundai. And yes, the bypass would have to be directly wired to the remote start so it knows when to turn on.

Thanks a lot, great info.