Karl,
That picture is one of your swaybar bushings. Can't tell from the picture if it's from the front or back. If you are complaining about the nosie in the
back, the steering wheel should have nothing to do with it. That bushing does look dry-rotted, but it may still be doing it's job. The best way to check is to jack up the rear of the car and support it safely on jackstands. (I DO MEAN SAFELY!) Then get underneath the car and try to move the sway bar up and down. Do you hear the clunking noise? If so you need to replace those bushings. There is one on each side. Also try to move the swaybar from side to side. If you can move it easily, the bushings need to be replaced to fix that. These are cheap parts; about $10-$14 each at any auto parts store. You just have to remove that one bolt, but soak it in a good penetrating oil like PB Blaster for a while first. You don't want that bolt breaking.
Other things back there can cause a clunking noise. A bad strut or the upper strut mount. A bad swaybar end link or even a bad rear lateral control rod. There are 2 rear lateral control rods on each side of the car. It's usually the rear most one (the one with the sleeve for the rear alignment adjustment that goes bad). You might be better to have that friend take a look to determine what is actually bad back there.
Look at this recent thread for a picture and a discussion on the possible noise form the rear lateral control rod:
Rear wheel at passenger side moves. Need Help!!
Mike