Except the scene establishes it wasn't her well.

It's established the BA in general don,t know compulsion. Liandrin's is a wilder trick, very limited. Verin's was pieced together with difficulty and over many years, from wilder tricks of wilder novices.

There never was any indication the BA knew any compulsion to teach.

Aran'gar had no ally among female Forsaken (Mesaana would sooner give the Tower to Aran'gar than teach her pet AS compulsion..), leaving only Cyndane and Moghedien. Moridin had no motive to have one teach Delana's pet compulsion, when Aran'gar herself could do any compelling there was to be done. Aran'gar's pitiful dealing with Egwene and her stubborness suggests strongly Aran'gar's skills there are not much.

And yet, not only Aran'gar tells Graendal Delana has been taught Compulsion, but also that she has decent skills in it. How exactly would Aran'gar know this, when did she have Delana compel anyone? That's pure out of the blue silliness, and speaks of a deus ex machina by Brandon.

If anyone ought to have taught Delana "decent compulsion", it should have been Graendal. Had Brandon not messed it all up, there probably was the Aran'gar/Graendal first scene in the prologue. It would make sense for Graendal to teach Delana compulsion, because Delana can Travel and could then go around compelling people or meet with Graendal's agents to mess up with Rand. It would make sense for Aran'gar to have accepted his pet was used this way by Graendal, because Aran'gar would have welcomed an importunity to learn more about Graendal's networks... and she sought to kill Rand.

But no.. .instead we got a Delana whose been taught Compulsion by nobody, Aran'gar midly impressed at her skills ("decent" in the mouth of a Forsaken means: "actually, she's quite awesome at it" while we've never seen Delana having any persuasion toward people Aran'gar ordered her to convince, so plenty of occasions to use compulsion if she's so good.. yet she never seemed to have used it.... and worst, perhaps, we have Nynaeve (cheaply, to reinforce the bloody red herring that Graendal did it to get his stupid cliffhnager) quite amazed at the complexity of the weave... she wasn't that impressed with Graendal's in Bandar Eban, for heaven's sake.

Really, the only good thing about this scene is that Graendal survived. Other than that, Brandon messed it all up, from the minutia to the back story, to the lack of set up to the misplacement of that scene, part of which belonged early in TGS, and the climax clearly belonged to the second part of the chapter when Rand balefired the palace.