Or a state-sponsored bounty. Though you don't want to encourage breeding them. Maybe reward all county taxpayers with a three-month-long tax holiday if they can be rid of nutria for a year.
They need to train dogs (very easy) to sniff them out. Man usually cannot detect them. This is how it's done in Germany, which has the very same problem when a lot got out of Danish farms.
Thats such a political argument, this is ecology, your POV on origins isn't correct in this case.
Introducing a new species that has never lived somewhere could maybe introduce really bad side effects?
Imagine a new predator that somehow eats everything and reproduce 10x more than any other species in the introduced ecosystem, causing it to simply be destroyed?
Same goes with plants, why do you think airports prevents you from importing fruits and seeds? Because they could cause irreversible damages.
You can Google tons of cases of invasive insects being mistakenly imported being a bane to farmers and the like.
I could use a new winter hat.
https://en.wikipedia.org/wiki/Nutria_fur