Remember that there is very strong tradition in the Tower to not interfere in another sisters' affairs. This extends all the way up to the Amyrlin Seat. The amazing thing is that the Hall actually thought they should control Moiraine's actions. I see it as a clear sign of the Black Ajah moving. By this point in time, they must have become aware Siuan and Moiriaine were present when Gitara died (this was no secret to women like Sheriam, who would have been debriefed on this). The Blacks must have been in panic mode because they had no one in Siuan's innermost circle. Siuan was scared enough that even dear friends like Sheriam and Delana were not part of her plans. The BA must have suspected that Siuan knows of their existence, as does Moiraine, and suspected that this must be why they were moving in secret over the DR.

The BA then more or less decided to let subtlety be damned. They actively tried to manipulate the Hall into throwing a wrench into Siuan's plans. Elaida obviously sent a letter to Galina when she sent one to the Hall complaining that Moiraine was messing with a ta'veren. Galina and Alviarin saw that as an easy way to ruin Siuan's plans. They played up the old Red vs. Blue rivalry, but had Talene give the Blues a true scare. They probably thought that even if the plan doesn't succeed, it would make Siuan more cautious, more afraid of the consequences of her actions. And they nearly succeeded, but for Moiraine heaping scorn on Siuan and re-energizing her. Seeing that Siuan was undeterred, and Moiraine was not to be curbed at all, Alviarin now ordered an assassination on Siuan, which failed due to Rand's ta'veren influence.