The whole point of Grizzleheim was to convince the bears to help fight against Malistare. But in the future we have to fight him on our own while the king doesn't do anything at all for the wizards who just saved thier world. Why should we help them anyways?
GH is a side world, that has no direct connection to the Malistaire storyline, you are helping GH from being destroyed by the "Raven Threat." This side threat to the Spiral is supposed to be resolved with the release of Wintertusk.
But no the bears and residents of GH do not help with the fight against Malistaire.