She really doesn't trust him as far as she could throw him, but the potential gain if he's willing to come through on his end of the bargain is enough to make her put that aside. Mostly.

"Very well," she says. Her voice is still a bit reluctant; it's her past as well, and not a glowing era of it, even though she doesn't much care what Sinclair ends up thinking of her. "And if you are true to your promise, I will consider this an unexpected windfall."

Asking Sinclair not to mention this to Jack would just give him more leverage over her. But she takes comfort that he doesn't seem to want to do so. Not if he needs Jack on his side.