It is invasive, but it's also easy to "prune". Just scoop a bunch out and throw it in the trash, or compost (as long as there's no risk of it ending up in a local body of water!). Your betta probably won't eat it, or if he does, not all of it. Just make sure it doesn't cover the entire surface so your betta doesn't have trouble breathing.
I keep water lettuce, which is very similar, with my two gourami and female betta, and they love it.
Here's my female "hunting" in the roots of my water lettuce: