To believe that Graendal saw Elza in TAR, apparently Delved her there and then taught her the necessary weaves to get the DM, because she figured that this would ultimately lead to a confrontation, where Rand will balefire Semirhage with the TP to protect Min. At least to me the idea that Graendal could foresee all this seems very far-fetched (similar to the idea that she figured out how Rand would try to kill her and fled before the balefire came).

I also think Graendal's involvement makes then only sense, if she closely worked together with SH, knew everything about Moridin's link to Rand and that Semirhage should be sacrificed. I don't believe, though, that Moridin would give this away, since it's basically a great weakness for him.

And why wouldn't Graendal visit Elza then in the real world and already cure her Compulsion, and avoid losing any time by teaching Elza those weaves, because Graendal could simply get the DM on her own & give it to Elza.

Besides that, BS didn't even said that Elza was taught any AoL weaves, but that Elza "had been given knowledge of several rarely known weaves", and this seems to be related to becoming SH's tool. To me this rather sounds, as if SH was responsible. We have other examples of people, who were obviously changed by the TP, e.g. Alviarin, Fain or Slayer.