her "interviews" with the captured Aes Sedai? I remember whoever was present thinking back to how many young channelers learned to manipulate subtly using the power, maybe making their fathers bring home a special gift or something of the sort. But, it was evident that she had much more skill than that. I could have sworn that was Verin and that she made Elza promise to protect the Rand until the last battle.
I suspect that whoever ordered Elza saw the compulsion weave and needed it to be remove in order for her to be able to take the second bracelet. I suspect SH as Moridin is just pissed at her failure and is willing to let her be captive with no rescue in the Forsaken meeting. SH also seems to take on odd jobs like this one.