I recently posted this http://blogs.starwars.com/STARWARSD2/16 And I just need to add a little clarification to what I said:

First of all, I'm talking about the lightsaber in ep 2 obi had when he was fighting jango fett...he brought that lightsaber with him to geonosis where in was taken away by the seps when he was captured....at the same time grievous had just been created in his cyborg form....Since he needed a weapon he was probably given obi's saber. Second of all, where you see obis lightsaber on grievous is not on the invisible hand in his cloak. I'm talking about on utapau when obi and the general fight. At the start of the battle you can clearly see obi's saber in grievous's hand.