wow does that pushing back and forward thing work? I got told that if
you want to kill a sick fish, you could just grab it's tail and pull
the fish backward through the water and it will drown them. Don't know
if it's true and never tried it...

Yeah I had a snail in a tank years ago with some assorted tropicals -
chances are with those antennae, they are going to get nipped from time
to time, but I'd say take it out away from the betta. Having said
that, maybe he'll get bored of it...