I recently pull the heatsink/fan assembly off my laptop (a Dell Inspiron 1121). The CPU had heat sink compound on it, but the southbridge and GPU had a square of grey putty. What is the putty? Should I replace it?
The putty is probably some kind of thermal transfer pad, it's not quite as good as heat sink compound but it doesn't need to be because it is intended to shift a lower amount of heat.
A larger heatsink that requires better thermal transfer which is afforded by being closer to the heat source and the heatsink compound which fills the gaps between the heatsink and heat source.
If there was a thermal transfer pad between the south bridge and heatsink assembly then you should replace it so the device does not overheat, while you should try to find a good pad that fits well, the selection is not as important as the heat sink compound.
3M have a range of pads and other suppliers can give you putty-like pads, choose something thick enough to make contact with both surfaces without too much pressure and with reasonable thermal transfer specs.
It could be Thermally conductive tape.
I'd say it's important to either leave the compound as intact as possible, or get new stuff that is designed for the intended surface and heat levels. I failed to replace those heat-conductors on the memory of a video card once, and it gave me rendering artifacts in return a few months later.