Rory is amazed that when she and the other students arrive at the Gilmore home in Hartford, Paris is already there, and greeting them as if it is her house. She and Richard clearly hit it off, and she seems to easily fit in with his plans and expectations, taking a prominent role as if she has indeed usurped Rory’s position as both group leader and granddaughter – although Richard is quick to remind everyone of Rory’s status.
This is an early hint that Paris has an affinity with older men – something which will become apparent later.
Rory says that the meeting takes place soon after 3.10 pm, but the school day doesn’t finish until 4.05 pm. This suggests that they are working during class time, even though they are meeting at Richard’s house. I’m not sure how they got permission for that, or if they even bothered to get permission. Maybe Emily fixed it up, since she is friends with Headmaster Charleston’s wife, Bitty.