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Every run of the mill garage door opener using rotating keys or nonces to prevent replay attacks. I assume any fob design worth its salt would implement something similar.

https://www.youtube.com/watch?v=CNodxp9Jy4A

I believe a nonce is used to prevent replay attacks, but wouldn't be surprised if there are some fobs out there which are vulnerable to replay.

It uses a challenge-response protocol, so you can’t simply record the signal and play it back.

It might not matter. If the point of the amp is to reduce the effective distance between the car and the fob, whatever messages are exchanged will look right to the car and the door will open.