Gemstone
In a lot of ways, the Gem was the center of a griffin's strength. In lore, it was known as a World Core.
The simplest ability of the gemstone was its Spiritual Sense. Others had to awaken their own, but the griffins had Spiritual Sense from birth. This was the earliest example of their influence on the world around them.
At its core, Spiritual Sense was just Spiritual Qi interacting with the world, blanketing it, and studying it. This process could then relay an image back to the host of the qi.
Griffins were able to exude this sort of pressure to interact with the world from birth, allowing them to see with far more than just their eyes. It was also this special Spiritual Sense of theirs that allowed them to understand the Order of the world in a way many couldn't even hope to. In this way, their gemstone was a lot like Ryu's Mysteries of Heaven and Earth Pupils.