Grass carp will eat it, but it's not one of their most preferred. Here's a primer on Chara.
It's a fairly low profile plant compared to others you might have. It pretty much hugs the bottom, maybe growing 18" off the bottom. It's an algae, so you can treat it without harming other species.
But, the real question is, "Should you treat it?" I'd say leave it alone unless it obstructs your ability to use the pond. It's great habitat for baby fish, it's not invasive compared to other plants, and it's a pretty good substrate for periphyton, which impacts your water quality in a good way.
If you were to treat it, odds are high that you'd end up with a plant growing there that you'd like even less.
If you do choose to treat it, wait. Right now it's at its toughest. Thick outside coating of lime, no access for herbicides to get inside, and it's not actively growing, and ready to go dormant for the winter.
Teach a man to grow fish... He can teach to catch fish...
