The CPE or customer premise equipment, viz., rooftop dish, lnb, STB, viewing card, etc., all belongs to the DTH provider. This is in the contract. This is true not just for Airtel, but also for DishTv, Tatasky, Videocon d2h, etc. When the contract is over, the DTH company can take back the equipment.
While the dish and cables are leased to you by Tata Sky, the STB is your property. You can sell it if you like. The card inserted into the STB is their property I guess.