After the brief exchange with Mr Chandler (and, he assumes, Sherlock; who else would it have been on the phone?), Peter goes back to his office.

Cal explained to Peter what he knew about Jarvis after the - encounter with with the ex-Reed Chandler, and it filled in a few small gaps that had been in Peter's knowledge of the Stark residence. Now it remains only to figure out how to contact a near-sentient AI without alerting said AI's owner. (That last was not part of his instructions, but Peter feels it can be assumed; Tony Stark has not, in his experience thus far, taken well to being looked after.)