Here's the carp info straight from WDFW: I didn't find the part about the grass carp, but this does clarify the common carp question:
"Further exacerbating these water quality problems, a large population of common carp has expanded unchecked in the lake and now dominates the biomass of the fish community, reducing resources for more desirable species such as trout, bass, and catfish. Common carp stir the sediments extensively through their foraging activities and resuspend the phosphorus. This behavior combined with the excretions of these fish is thought significantly diminish water quality. Furthermore, because of their rapid growth, Green Lake common carp rapidly reach sizes that make them invulnerable to the lake's resident predators."
I've e-mailed WDFW to get more info on the grass vs. common carp issue. As far as catching common carp - dough balls or yellow corn are all you need, slip weight on the bottom. Hang on if you hook a 20 pounder!