Yep this is just one kind of bladderwort. You can leave it in or tear it out, it wont grow THAT fast that it will cause a problem (at least not that kind). Its like a weed though, not something you would likely want to purposefully cultivate. It comes in with other plants as a small spec then grows into a big mess that looks kind of like javamoss but not as dense.
The kind you have will never be big enough to trap any fry, it will feed mostly off any bacteria and microscopic stuff in the water. As long as your tank has proper nutrients it wont harm the growth of any other plants. When I had some I left it in the tank, eventually something ate it all away, probably the crayfish.