He specified those two groups for a reason. Strange honestly doubts Rita will know anything important about the Severing but if she does, he's telling Nightshade right away. He's got to be careful to juggle his agreements, to make sure that he's not breaking one while casting another. It's a wonder how the fae manage to keep all these straight.

Still, as Rita agrees, that feeling of power in the air vanishes, as if it's settled. It feels like a weight has been lifted off of their shoulders and the nearby air as the binding spell sets it in place. Strange knows that even if he wanted to tell the Circle what had happened in this conversation, he couldn't.

At Rita's question, Strange frowns slightly. "I'm trying to find information on a particular event. Considering that the Circle might have been involved in this particular event, it's best that they don't know I'm asking about it. And I'm doing it behind the Council's back because I don't want those jackasses to even look my way."

Is it a bit cowardly? Yes. But in Strange's mind, this is entirely self-preservation, not cowardice. You don't tell the people you're trying to fuck over that you want to fuck them over to begin with.