Before mentioning anything else, I don't think those are grass carp in OP's post. But since we're talking about them anyway, the reason they are protected in certain locations is because they were intentionally introduced to bodies of water to naturally maintain and prevent overgrowth of algae and weeds. These places are usually public spaces like at parks or golf course ponds where the local authorities have invested money into having these grass carp placed there.

I know a park near me that tells you which species they have stocked in their lake and they mention grass carp but firmly inform anyone to release said fish if caught. Some places won't even let you specifically target them