You can try to detect the amplified signal, and if you put an accurate timer in the fob you can make it take exactly 5000ns to process and then require a signal back within 5020ns.
Detecting the amplified signal won't work. There are these things known as directional antennas...
The timer idea is a good one, although a ns-accurate timer is starting to get a bit much for something to put into a key fob. Especially give it's run off of a watch battery (power requirements) and often exposed to heat / cold (thermal drift).
Dylan's comment requires a timer in both the key fob and in the car. The key fob to delay transmission of the challenge response, the car to check if there isn't too much delay in the challenge / response pair.
You really need a timer in the key fob, as the processor in the key fob is often so slow (for battery / cost reasons) that an extra couple clock cycles somewhere would throw off the timing enough to make it fail.
Cool trick in that one, the Prover(i.e. the key fob) does the distance measuring part of the challenge response protocol using analog only components. This means its response time is <1 nano second.
So you can do it with only the car having a good timer.
Well for the example timing I gave you only need 1 part per thousand accuracy, and it's easy to get 10ppm or much better. It only needs to run during communication, anyway.
