The phrase "reservation line" refers to a dedicated phone number or conduit that allows people to reserve or book something like a hotel room, flight ticket, or table at a restaurant. Full definition
Once the reward is issued, we handle the guest's entire hotel itinerary through a dedicated reservation line. (travelcodex.com)
Finally, when it comes time to make a hotel reservation, do so through the hotel's website or direct reservation line. (creditcards.com)
You'll need to look out for fuel surcharges on some flights, as well as navigate a phone reservations line to book flights with partner airlines. (creditcards.com)