Or it's literally that Quantum was an underling of Spectre and disbanded following the Bolivia affair. Although it does appear that EON has done their best to basically write Quantum of Solace out of existence. Greene gets one brief mention, but neither he, nor Fields, are shown in the photos when Bond is moving through the wrecked Vauxhall building.
I'm not a fan of Quantum of Solace by any means, but I was a little irritated on how there was virtually no mention of Fields, whose death is due to Bond bringing her on his little revenge mission. They did mention Greene, but as you said briefly. Found it funny how Greene and Fields weren't part of the titles sequence nor the wrecked Vauxhall building either.
I thought Greene did show up in the titles... I might be imagining things. Must see it again.