Because this wasn't spurred by his letter to her so much as by the fact the army showed up. She had to be seen dealing with the matter publicly and officially, as Queen of Andor. She sent an official envoy (her chief clerk is a kind of prime minister too) with rules this foreign army known to be tied to Rand must adhere to to be allowed to remain, because that's what she had to be seen to do. She took similar steps about Taim and the BT, and make a public show that they are allowed near Caemlyn not on Rand's authority but at her sufferance.

She could neither afford to do anything less nor anything more... She could not send Birgitte for this, it's a job for a court functionnary. Norry had no secret message, because Norry doesn't know about Elayne's real ties to the Dragon and his associates, and because Elayne couldn't know who would be keeping an eye on Norry. She went by the book, for all eyes to see. She won't contact Mat for a while - she'll contact him once people at court have all but forgotten he's there.

Mat is a bit thick not to have understood from Norry's visit that his presence near the city was causing political problems and Elayne could not afford to show any ties to him right now, and certainly not give answer to any request to commit resources.

Thom seems to have gotten the message right away - Mat is being obtuse and quick to see in this a personal affront, as he so often is (it's a trait of his character, he very often doesn,t understand the subtleties of what's going on with anyone, especially AS, Elayne and Rand... he's out of their league). He's just not sophisticated enough to catch on, military stuff aside. He should ask Talmanes - a Cairhienin like him wouldn't need any more than Norry's visit to understand perfectly what's going on. Mind you, the way Thom acts, he seems to have tried to explain and is just bored with Mat rejecting his explanation it's politics and insisting to see an affront in this. When Mat refuses to understand, you just give up. Nothing you say will convince him he's wrong.