Yet we didn't really know Slayer's full nature until much later. Even his "job" as Shadow assassin was vague at best until much later when he tells us.

We did know Graendal had knowledge of Rands timelines, had plausible reason for being in the Palace, would recognize Asmo on sight and had the means to kill him and vanish with non the wiser. Reversed weaves and masked ability would ensure Aviendha wouldn't have felt her Gateway or potentially Balefire.

One more reason I have that comes later in the series is that Slayer doesn't reveal killing Asmo when he thinks back on his "prized kills". In contrast, Graendal often thinks about the other Forsaken and either knows what they are up to, or complains that she is unaware... oh and she's fully aware that Asmodean is dead since she knows there are only 8 left...

TGS
Prologue

That man frustrated her, though she would never admit it out loud. Mesaana was in the White Tower, pretending to be one of what passed for an Aes Sedai in this Age. She was obvious and easy to read; Graendal's agents in the White Tower kept her well apprised of Mesaana's activities. And, of course, Graendal's own newly minted association with Aran'gar was helpful as well. Aran'gar was playing with the rebel Aes Sedai, the ones who were besieging the White Tower.

Yes, Mesaana did not confuse her, and the others were equally easy to track. Moridin was gathering the Great Lord's forces for the Last Battle, and his war preparations left him very little time for the south—though his two minions, Cyndane and Moghedien, occasionally showed their faces there. They spent their time rallying the Darkfriends and occasionally trying follow Moridin's orders that the two ta'veren—Perrin Aybara and Matrim Cauthon--be killed.

She was certain Sammael had fallen to Rand al'Thor during the struggle for Illian. In fact—now that Graendal had a clue that Semirhage had been pulling strings with the Seanchan—she was confident she knew the plans of every one of the other seven remaining Chosen.

Seems odd that Graendal knows he's dead (she qualifies her thought on Sammael, but not Asmo) when no one else is at all sure.