Woody and Buzz run into these guys inside one of the games at Pizza Planet. There's a whole colony of them living inside a crane machine game where they worship The Claw as their lord and master:
BUZZ: Who's in charge here?
GREEN ALIENS: The Claw! The Claw is our master. The Claw chooses who will go and who will stay.
WOODY: This is ludicrous.
Okay, we don't have much to say about these guys except they're…true believers. They all live together until The Claw grabs one of them up and sends them to the outside world, so it totally makes sense that they would have come up with what's basically a whole religion around being chosen by The Claw. Just like the toys in Andy and Sid's room have their own little societies and ways of dealing with things, the little green aliens have their system, too.
It's kind of sad though because we know the salvation the little green aliens are spewing is just snake oil. The tiny dude that goes home with Sid is so psyched—"Nirvana is coming! The mystic portal awaits!"—but the audience already knows Sid's house is no kind of heaven. It's hard when your mythology lets you down.
But, still, we love these little guys and we're not the only ones. Joss Whedon, who co-wrote the screenplay for Toy Story, recalled that these little guys were one of the last characters added to the movie and that they're "the thing I most wish I could take credit for." (Source)
Hey, Joss: you'll always have Buffy.