Gren, like many characters in Cowboy Bebop, is a wanted man. This of course means that info one doesn't usually know about fictional characters was displayed prominently on the screen. So in case you were wondering, here are his stats:
Name: Grencia Mars Elijah Guo Eckener
His crime of course is breaking out of prison. It's not entirely certain what the amount on his head is, but according to the statute of limitations Gren's bounty, which is about to expire after three years, is double its actual amount making it a hefty sum. That also implies that he's been on Callisto for three years, assuming that he went there straight after his escape.
As well, although it says he is from Callisto I don't think that means he was born there. If anything, I'd say he was from Mars because in all the pictures of his early life he was in a warm environment that is quite unlike Callisto and seemed rather well off money-wise. Plus he was in the same unit as Vicious, who is from Mars. Please note that this is just my opinion and not actual fact.
As a side note, The role of Gren was voiced by Kenyuu Horiuchi. I can't say I know him very well, but I think he did a wonderful job playing Gren with great dignity. Some of his other roles include Daley (Bubble Gum Crisis), Taki (Captain Tsubasa), Sanson (Nadia - Secret of Blue Water), and Bishamon-Ten (RG Veda). Full information can be found here.