Hey everyone. I'm a little late to the game here. I'm an invasive species specialist for UW Sea Grant and Extension that lurks on the forms with the intent of going fishing someday....and then I don't haha. Anyway, I might be able to clear a few things up.
As someone previously stated, grass carp are part of the four species of "Asian Carp" that include silver, bighead, grass and black carp. They all eat a lot and get really big, but they all eat different things. Silver and bighead carp are filter feeders and eat plankton, grass carp eat aquatic plants, and black carp east mollusks (snails/mussels). Regardless, of what they eat, they all have the ability to negatively impact food webs.
Silver (the jumpers) and bighead carp are the ones you often see on the news, and are the ones we are concerned about swimming through the Chicago Area Waterway System into Lake Michigan. Grass carp have been found reproducing in the Maumee River, a tributary of Lake Erie.
One reason grass carp were brought to the US was for biological control of plants - again, they eat a lot. However, due to their potential impacts, most states have made it so only sterile grass carp can be used or (like Wisconsin) have outlawed their use completely. Since the Wind Lake fish was sterile, it was almost certainly purchased from a producer somewhere and either intentionally released or it escaped another setting. There are likely places not too far away and outside of Wisconsin for someone to legally purchase grass carp.
Regarding possessing an invasive species - again, someone mentioned this, but a key factor is whether the specimen is alive or dead. Something ceases to become invasive once it's dead. In some cases, like for fish, that is easier to assess. In other cases, like plants and mussels, it's tougher since mussels can survive days out of water and small fragments of plants can start new populations. There are exemptions for disposal and for transport for identification.
Hope some of that helps!