They need to make sure 'unclean' arrivals to not mix with clean departures at A so do check the train is empty there.
There is no need to worry about clean departures mixing with unclean arrivals so no check at C, but once in the unclean arrival stream you will be considered unclean and need to reclear security to get back into departures.
a to b to c to b to a is fine, (clean to unclean)
C to b to a to b to c is a problem (unclean to clean)