I note that Claudia is careful to make it clear she's "not supposed to be curious" about what the orders for Elizabeth she's handing over from the Centre are about, i.e. that she does not know anything of the matter.

I thought it was Claudia's way of fishing for info. "I'm not supposed to ask" isn't the same as "you're not supposed to tell me". There's a slight pause after that sentence, and then Elizabeth moves on to a different topic.