Tribal Heritage and Grizzly Bear Protection Act This bill prohibits a person from taking, possessing, or transporting grizzly bears ( Ursus arctos horribilis ), or their parts. The bill does not apply to: (1) grizzly bears, or their parts, if they belong to a population that is listed as a threatened or an endangered species under the Endangered Species Act of 1973; (2) grizzly bears, or their parts, taken, possessed, or transported in Alaska; or (3) takings that are imminently necessary for self-defense or to save the life of a person in immediate danger. The term "taking" means to harass, harm, pursue, hunt, shoot, wound, kill, trap, capture, or collect, or to attempt to engage in such conduct. The bill establishes civil and criminal penalties for violations. The Department of the Interior may issue a permit for taking, possessing, or transporting grizzly bears, or their parts, under certain circumstances. However, Interior may not issue a permit if the taking would cause the total mortality for any population or subpopulation of grizzly bears to exceed the scientifically recommended limit determined by the Interagency Grizzly Bear Study Team. Interior must establish a demonstration program of grants to states and Indian tribes for assisting livestock producers in undertaking non-lethal activities to reduce the risk of livestock loss due to predation by grizzly bears and providing compensation for losses due to the predation. The bill provides for the reintroduction of grizzly bears on tribal land.