LORELAI: You’re seriously gonna run all over town looking for Jess and Rory?
LUKE: If I have to, yes. And if you were really a concerned mother, you’d go out there with me.
LORELAI: No, I can’t do that. But if you like, I’ll let you sniff Rory’s sweater. Maybe her scent will help you track them down.
Lorelai compares Luke to a bloodhound, which can be trained to track people after getting their scent from clothing. Comically, Luke does take Rory’s sweater with him, but it’s not to sniff, it’s because he’s worried she might be cold.
The Annotated Gilmore Girls 