I tried to think of the most harmless thing. Something I loved from my childhood. Something that could never ever possibly destroy us. Mr. Stay Puft! - Ray
I think of Griever as Squall's Stay-puft marshmallow man except in this case Squall wasn't thinking of a (supposed to be)harmless being but rather the most powerful guardian foce. Ultimecia knows that Squall regards Griver as the most powerful GF. As previously referenced from the scan, it seems to be public knowledge:


Griever
In Squall's mind, the strongest GF.

I think Ultimecia wanted to intimidate Squall by forcing him to face what he regarded as the most powerful force. At least in the GF world.
Griever was probably one of my favorite bosses in that whole game. The look, the music and the difficulty were all great.