Is it a v8 car? If so, you might consider upgrading to an 8.8 rear end. Your's should be a 7.5, which is fine until you start making a little power. Regardless, you can remove that extra stuff. When I was young, I always thought they looked cool hanging down behind the 82gt. But they're not very useful. They were designed to help eliminate wheel hop, but my understanding is that they didn't work very well. A better solution is to buy a good set of aftermarket lower control arms. Remove the upper control arms and weld a plate to the open side to box them in. You want the uppers to flex a little, which will help save your torque boxes... which are known to tear under stress. Another option, if you decide you need it, is to use aftermarket uppers and lowers, but only after installing torque box reinforcements or "battle boxes". If you're not making a lot of power and don't plan on hard launches, then I would suggest aftermarket lowers and boxed factory uppers. This should eliminate wheel hop, for the most part.
FWIW, the quad shocks barely did a better job than the anti-hop bars, from what I've heard.