As the other educator points out, the author never explicitly states an answer to your question. However, we can make an informed guess as to the most important insight Momaday gained about his heritage during his pilgrimage to Yellowstone and his grandmother's grave.
In the prologue, Momoday highlights the importance of his journey to Rainy Mountain. He points out the beauty of the landscape before him and draws attention to a passing era in history, one which so clearly captured the essence of the human spirit. For Momoday, the migration of the Kiowas from the Great Plains toward the southern portions of Yellowstone is a testament to the endurance of the human spirit.
The Kiowas befriended the Crows along their journey, and they also acquired horses. These horses transformed the Kiowas from a nomadic people into a formidable race of hunters. Momoday tells us that of all the tribes on the Plains, the Kiowas owned the greatest number of horses per person. The horse allowed the average Kiowa warrior to excel in tracking down and hunting buffalo and deer.
Throughout his story, Momoday pays tribute to the adaptive nature of the Kiowas. His people adopted the sun religion of Tai-me and learned to participate in Sun Dances as they moved south. So deep was their religious conversion that, even when the buffalo died out, the Kiowas stubbornly clung to their new religious traditions by substituting old buffalo hides or even horses in their rituals. The Kiowas celebrated their Sun Dances until the last of the dances were dispersed by United States Cavalry soldiers. Momoday reiterates that his grandmother never demonstrated bitterness regarding the fate of her tribe. She lived on, adopted Christianity as her new religion, and adapted to new ways, just as her tribe had always done.
Momoday recounts the Kiowa history with awe as he journeys to Yellowstone and his grandmother's grave. Essentially, the most important insight Momoday gains about his heritage is that the Kiowa spirit is eternal in nature: the human capacity to survive and to thrive continues even though the tribe is no more.