They are not native.
Read this article from 2005
http://www.anapsid.org/floridaiguanas.html
"Wildlife officials approve of Johnson's trapping and euthanizing methods, which Johnson said are a lot more humane than what private homeowners were doing to the lizards. Although iguanas are not a protected species, state animal cruelty laws do apply."
So is it cruel to kill them or just to cause them harm for no reason?