As a sales promotion, the rebate offer reflects the fact that Internet connectivity, not television, is becoming the core part of the business for companies like Time Warner Cable. But it doubles as something else: as a shot across the bow to cable programmers who say that distributors should pay them more for the right to such place-shifting. Time Warner Cable has been wrestling with programmers for months over this issue. In March, the company released an app that allowed its paying subscribers to watch dozens of cable channels on the iPad at home. The app was challenged by some programmers, led by Viacom, which owns channels like MTV and Nickelodeon and which accused Time Warner Cable in a lawsuit of “unlicensed distribution” of its content. Time Warner Cable, in its own lawsuit, argued that its existing carriage contracts with companies like Viacom cover all the screens in a subscriber’s home. The dueling lawsuits demonstrate just how contentious the topic is for the television industry. “Both sides see their own future as being up for grabs,” said Dan Cryan, the senior principal analyst for broadband at IHS Screen Digest. Distributors are trying to make sure they keep pace with consumers who want to watch TV in new places and on new devices. Programmers are trying to make sure that they don’t miss a major revenue opportunity.