I often see it wrongly stated or implied that Graendal's main task given to her by Moridin in TGS was basically giving Rand "pain of heart". However, this isn't what Moridin actually wanted Graendal to do above anything else.

In the prologue of TGS, Graendal says:
"I live only to serve the Great Lord."
"Then serve him in this," Moridin said, looking directly at her. "Al'Thor moves for Arad Doman. He is to live unharmed until he can face me at that last day. But he must not be allowed to make peace in your lands. He will attempt to restore order. You must find ways to prevent that from happening."
"It will be done."
"Go, then," Moridin said, waving a hand sharply."

This command is obviously what Moridin mainly wants from Graendal, namely preventing order in her lair Arad Doman (since if chaos rules, the Pattern become instable, and the DO's influence grows stronger).

Then - as an afterthought - Moridin also reminds Graendal of another goal of the Shadow, before she leaves:
"And Graendal [...] The end is near [...] The Wheel has groaned its final rotation, the clock has lost its spring, the serpent heaves its final gasps. He must know pain of heart. He must know frustration, and he must know anguish. Bring these to him. And you will be rewarded."

Contrary to Moridin's imperative command regarding Arad Doman, the giving of "pain of heart" to Rand is rather an optional task for Graendal, that would give her some reward if she will do it. Probably, like spreading chaos or searching the seals, this long-standing task of giving Rand pain of heart is known to all Forsaken (Graendal just nods, when Moridin mentions this goal), and all of them would be rewarded if they contribute to this. But no one of them has the sole mission to break Rand. If this is the main goal for one of the Forsaken, we can suspect that Moridin himself would do it. It's in any case clear, that it's more important for Graendal to keep Arad Doman in chaos, than demoralizing Rand.

Consequently, this also reduces the chances that - as some theorize - Graendal was involved in freeing Semirhage to have her balefired by Rand, or that she wanted Rand to balefire her own palace, since it isn't directly related to preventing order in Arad Doman, but rather related to giving pain of heart, which as far as we know isn't Graendal's main concern. Considering that Graendal doesn't want to face Rand, it seems unlikely that the hope of an unspecified reward would convince her to attempt something that would likely bring her near Rand to give him possible pain of heart. Of course, preventing order in Arad Doman was a direct command by the Nae'blis, thus Graendal had to stay there.

For these reasons, what Granedal plotted in TGS, was rather simply how to keep Arad Doman in chaos, e.g. by manipulating the nobles or other important people, than that she was involved in a risky plan to break Rand.