Here’s how I understand the issue:
A keyfob is a radio Transmitter. To unlock your car you need the radio transmission to reach the car. The keyfob doesn’t transmit a signal when at rest. Therefore putting a keyfob in a Faraday bag achieves nothing.
Modern fobs should be designed to prevent replay attacks (there should be something specific in the request that alters the response), so it shouldn’t be possible to record a response and then use it later.