First, to clarify, they have a staff member who has received GIA education prepare an appraisal certificate for your pearls. It is not a GIA certificate and GIA does not train people to assign a letter grade to pearls. Pearl Paradise has all their staff GIA trained in pearls and they send an appraisal too. It's a nice extra to have. The Gemological Institute of America does pearl reports, not certificates. I'm only saying this because I see confusion on this a lot.
Roman, go back and click on the link I posted and look at the photo of the two grades together. You can see that the AA is kind of a button shape and the AAA is very round. Also, there is a better surface quality on the AAA, which appear darker and bluer in the photos.
The World Is My Oyster!