For (literally) years, people have been dancing around this idea. "What motivation would she have?" Murders do not require a motivation. They require opportunity and means. We know full well that Graendal has the means. She's an extremely strong channeler who knows exactly how to do whatever she wants in the (literal) blink of an eye.

As per opportunity, there have been many theories back and forth for why she was in Caemlyn. Some say to go through Rhavin's stash of goodies. That's a distinct possibiliy, seeing as how she did that with Sammael. But you know what's far more likely? She was already in Caemlyn. Remember that Lanfear, Graendal, Rhavin, and Sammael had a plan to lure Rand to attack Sammael in Illian. They had been goading him for some time. The plan for for Rand to attack Sammael in Illian, and Rhavin, Graendal, and Lanfear would join in the attack and it would be over.

From their point of view Lanfear was a no show. Graendal had every reason to be in the Caemlyn palace for that plot alone. She had to know that the battle between Rand & Rhavin didn't go well. It was time for her to get out of Dodge. She walks out. Literally the only person we know for sure who would recognize her is Asmodean. At that point, we can't even be sure if Rand would recognize her (although I suspect that he would). No Aes Sedai would....even if there were any in the Palace (which were were not). It was just Asmodean's very bad luck to stumble across her while she's trying to escape. Not only does he see/recognize her, but she also believes him a traitor. Click...click...boom.

Asmodean's toast; Graendal gets out of the palace with no one the wiser.

I don't understand what's so hard about this thought process.

~Jeordam