I will try to answer off the top of my head, and I hope it's close enough. They currently say very little about the subject as newer and newer evidence pours in. They lean on their old understandings and misconceptions that carbon dating is wrong because of the flood, DNA is real but only proves how marvelous Jehovah is while using it for backtracking anything is just 'theory,' there is only a small amount (about enough to fill a large coffin or footlocker) of actual fossils that reflect creatures that were not quite like modern humans. They said that science is driven by the need for funding and archaeology is full of nonsense theories and hoaxes and that the scant fossil evidence is largely from a few deformed or inbred human beings who are not millions of years old but miscalculated (because of the flood again), while the vast majority of normal fossils are simply ignored.
If they have any updates to this, I would be surprised. Even the Pope is backing down on this in the face of overwhelming new evidences and how well the Human Genome Project is filling in the blanks.