I did some more searching about these grass carp and found this. Notice one of the lesser preferred weeds that they eat is milfoil. They also don't like to feed around swimming areas, and can promote algae blooms in some cases.

Grass carp:
Are only distantly related to the undesirable European carp, and share few of its habits.
Live for at least ten years and probably much longer in Washington waters.
Will grow rapidly and reach at least ten pounds. They have been known to reach 40 pounds in the southern United States.
Feed only on plants at the age they are stocked into Washington waters.
Will not eat fish eggs, young fish or invertebrates, although baby grass carp are omnivorous.
Feed from the top of the plant down so that mud is not stirred up. However, in ponds and lakes where grass carp have eliminated all submersed vegetation the water becomes turbid. Hungry fish will eat the organic material out of the sediments.
Have definite taste preferences. Plants like Eurasian milfoil and coontail are not preferred. American waterweed and thin leaved pondweeds are preferred. Water lilies are rarely consumed in Washington waters.
Are dormant during the winter. Intensive feeding starts when water temperatures reach 68o F.
Are a river fish and have the desire to move from still waters into flowing waters.
Are difficult to recapture if a waterbody has been overstocked.
They may not feed in swimming areas, docks, boating areas, or other sites where there is heavy human activity.

Advantages
Grass carp are inexpensive compared to some other control methods and offer long-term control, but fish need to be restocked at intervals.
Grass carp offer a biological alternative to aquatic plant control.

Disadvantages
Depending on plant densities and types, it may take several years to achieve plant control using grass carp and in many cases control may not occur or all submersed plants may be eliminated.
The type of plants grass carp prefer may also be those most important for habitat and for waterfowl food.
If the waterbody is overstocked, all submersed aquatic plants may be eliminated. Removing excess fish is difficult and expensive.
If not enough fish are stocked, less-favored plants, such as Eurasian milfoil, may take over the lake.
Stocking grass carp may lead to algae blooms.
All inlets and outlets to the lake or pond must be screened to prevent grass carp from escaping into streams, rivers, or other lakes.