The TARDIS watches Rin carefully at first, until she's reassured that it seems to know what it's doing - or rather, is able to follow her instructions accurately. Then she more closely inspects the drone feeds, working on creating an accurate map of the boat. While she'd been teleporting around earlier, she hadn't exactly been paying careful attention to her surroundings.

And then it offers to share the feed, and she accepts curiously. Normally she might not be too interested, but given that Rin is definitely also from a different universe than her own N-space, it's actually somewhat interesting.