Quinn must go to the FeatherWind spire, the roosting place for wild War Griffins.
It is a plateau looking thing with a rock spire twisting out of one side; imagine a square table with a tall vase set above one of the legs. There, now you have a mental picture of the FeatherWind spire.
He has to go retrieve an egg, which is wayyy dangerous. The War Griffins have serrated talons, toothy beaks, and their wings are often used for powerful bludgeoning. their eyes are known to paralyze weaklings. The eggs are kept at the top of the spire, so any egg thief would be easy to spot and easier to deal with. And if a thief managed to sneak past undetected, the climb would be very dangerous.
Yahante, Jasmine and Cayde would be allowed to accompany him to the Spire, but not assist him with the actual retrieving of the egg; unless Opheliah says they have to stay at the palace, in which case a guard would escort him to the spire. His proof of completion... well duh, he will have a War Griffin egg. It must be unharmed, no cracks or blemishes, or the quest is forfeit.