Probably they are not invasive in TN, but for sure down here where the winter temps don't kill them back, they are a highly invasive species and we'd love it if the squirrels would eat them.
Are the squirrels getting IN the water to get at the plants, Gail? If not, it's possible that a scent deterrent of some kind sprayed on the foliage might stop them from grabbing the plants to pull them out of the water. I've used "Critter Ridder" which is a pepper based scent deterrent available at HD or Lowe's. There's also an entirely organic granular one we used when we had a rabbit problem at the school garden. You could sprinkle it around your pond for a few weeks to send them elsewhere. Sorry, can't recall the name, but again, I got it at Home Depot.
