It's tempting to play with the touch screen to make sure everything is working before you start putting things back together. Remember the home button will not work until the touch screen is seated properly in place.
The GSM component is glued to the screen with different adhesive (more like glue). I managed to not damage this but it was really tricky. The guitar pick is too thick and weak to release this from the screen. Id recommend you wait until you lift the glass (future step, NOT NOW). Then, with a good light you'll see the white plastic adhered to the glass. A thin metal pick or exacto is needed to patiently cut & pry your way through the adhesive. Careful of the camera as your pulling in that direction.
I cut through my wifi cable partially, but it still works (surprisingly). I'd recommend staying well clear of this with the pick. When you go to lift the screen (future step, NOT NOW), use a really good light, start to lift the glass slightly at the corner and you will be able to see the cable. Then you can heat it more and watch the cable as you pull through the adhesive there making sure your not catching the cable.
Like others i found the plastic tool pretty useless. Exacto, razor blade, or small metal pick/pry tool works much better to get that first guitar pick inserted. Be careful not to damage the bezel too much. Unless to plan to replace it.