Incorporate minigames into the companion app to unlock items in game.
So, how about incorporating some kind of mini-game into the companion app that would allow players to earn items for the main game. I'm not thinking anything game breaking like exotics or legendary gear - or any kind of gear for that matter, really, but it might be nice to have a Destiny themed mini-game to earn materials or unique shaders/ships/sparrows/ghost camos. Nothing game breaking and perhaps not necessarily "exclusive", but some nice perk or reward for playing. Not only would it give players another avenue to connect to your game, but it would also incentivize them to download and use your app (which I'm sure your marketing team could find a use for). It's a win-win.
If you're worried about having the development staff to put together a mini-game, I'm sure somewhere in Activision there is a team looking into mobile apps or maybe you can license and re-skin an already existing game.