"We let you go after the interrogation, didn't we?" That's not a good reason to trust someone and Strange knows it. There's a pause, as he tries to mull more sound reasoning over.

"Besides, who else is going to solve this? The Circle's a widespread organization with plenty of resources and even more manpower. We're the best hope at figuring this out." The demons are moving in and the Rose Queen only cares about her own. Strange might not fully trust the Circle now, but he still realizes it's the best hope for actually piecing out what's going on. So, he continues to lie his ass off.

"And, like I said, we're already enough into the investigation that they've assigned someone to look into it. Do you really think anybody else cares enough to even do that much?"