That doesn't fix this exploit at all: This is merely an analog device amplifying other radio waves.
The only way to secure against the described exploit is to measure round-trip-time from the car -> key -> car and ensure it's under, say 5 light-meters: aka 16 nanoseconds, plus the carefully calibrated time it takes the key to compute its response.
16 nanos is a very short amount of time, and it'll be tricky to measure that reasonably accurately.
The real solution is to require the user to interact with the key in some way, like pressing a button, or perhaps moving it around (as would happen as you walked with it in your pocket).