OK, so basically there are other lines of evidence that indicate the Giant Impact happened. For example the fact that earth is tilted on its axis, or the fact that Earth might have a denser core than Venus. The impact would have also been during a time when planetary bombardment where very common, so it's really not something unusual and we've seen similar things happen in other solar systems.

The geochemistry comment basically refers that's to the fact that the isotopes that make up the minerals on the moon don't quite line up with that we would expect from the merge.  You would normally expect the earths crust and the moon's to have different amounts of elements because the earth has differentiated (i.e. Lighter elements have become concentrated in the crust), but one thing you wouldn't expect to see a difference is the isotopes of an element like oxygen in the moon and earth rocks if they had the same origin.

If there was a mix between 2 planets, and that mix was uneven, then the rations of isotopes would be be different between the earth and the moon, unless the mixing was complete. I'm not an expert on this, so I can't comment on the exact status of these ratios, but I do know it was regarded as something that people were fairly confident would be worked out within the model of the Giant Impact. Earth is a very complex and dynamic system, so discrepancies in this regard could easily be explained by some sort of internal process that we just haven't observed yet.

Hope that's some help!