While Dean is changing the water bottle for Lorelai on the back porch, Rory comes out to talk to him. (Apparently the Gilmores always drink bottled water – I don’t know if the Stars Hollow water supply is undrinkable, or if Lorelai and Rory prefer the taste of bottled water, or drink it for health reasons, or some other reason. Much of the Connecticut water supply has chromium-6 in it, the cancer-causing agent that featured in the 2000 biographical film Erin Brockovich, but the official statement is that it is at levels too low to be dangerous. The Gilmores may be playing it safe, especially as eleven other cancer-causing agents have been detected in the Connecticut water supply at levels above the legal limits).
Rory invites Dean to come with her to the special dinner her grandparents are giving in her honour. Emily told Rory she could “invite her friends” to the dinner, probably meaning her “friends” from Chilton (Emily doesn’t know that Rory is currently at outs with the few friends she has made at school). She almost certainly did not mean Rory to invite Dean, who she last saw taking Rory to a school dance, which ended in disaster when the pair of them fell asleep and didn’t get home until dawn.
Dean has the good sense to point out that Rory’s grandparents probably aren’t madly keen to see him again, but eventually accepts Rory’s invitation to please her (their relationship has only just re-kindled, and he probably doesn’t want to start off by saying no to her).
The scene is shot almost like a proposal – Dean is kneeling at Rory’s feet with the water bottle, while she holds out her hands in supplication, as if ready to receive a ring. It’s a reminder that Lorelai never got this traditional down-on-your-knees proposal from Max. If you look at how happy and excited Rory appears at the thought of taking Dean to her dinner, it’s in stark contrast to the sad, anxious face Lorelai has when we see her and Max getting engaged over the phone.
The show seems to be saying, “This is what you deserve, Lorelai: this is how happy you should be”.