Without reading, I first thought the postcards would be in the bags of rice, and then by going on which postcards were (or weren't) returned, they could see the areas where corruption was preventing people from getting their rice.
That was my initial guess as well, but I was a bit confused -- unless bags of rice were getting destroyed without being opened, it would be pretty easy for corrupt distributors to send back the ACK postcards anyway. This out-of-band checksum should be harder to compromise.