The Greevil made their first appearance in the E3 2006 B-Roll. There was creature editor footage of the Greevil changing its hands and feet. Also, this was the first demonstration of the texture editor and showed just how many parts were added since GDC '05.
The next time the Greevil showed up was in the E3 2006 demos given by Will Wright, after the main species, the Screeble, traveled to one of their colonies. The colony was actually a moon orbiting a Gas Giant. The Screebles launched Fireworks and wowed the colony. They began worshiping the Screeble ship.
Once Will Wright abducted one of their kind and accidently dropped and killed him, they began attacking. They attacked through Laser Turrets. Will Wright demonstrated some weapons, including the Laser, what appeared to be a plasma missile, and an Ice comet, normally used for Terraforming. The City defense were soon destroyed and the Screeble UFO pulled out.
After the Screeble UFO won the battle, it was contacted by the Greevils, informing the UFO that the city they had just attacked was only a colony and that they were going to launch an attack on the Screeble home planet. The UFO apologized and admitted it was an accident, but a transmission arrived from the Screeble homeworld informing the UFO of an attack. The UFO rushed back to its home planet. What happened after that is unclear.
According to the Screeble's Column rare, the Screebles were the greatest civilization in the universe. If they expanded like that, they probably defeated the Greevils.
The Greevil bear a strange resemblance to ALF, and there may be a distant relation there.
A similar creature, named the Wee Greevil, appears in the complete version of Spore.