Whenever I set up a part of a trip in TripCase, I make sure that I include a phone number (or that a phone number is a part of the imported itinerary). That way, if I need to contact the airline, hotel, restaurant, attraction, etc., all I need to do is click the phone icon above the segment in the trip. No fumbling for the number, looking it up or calling directory assistance needed.
If your trip item is automatically imported into TripCase, this will likely be done for you. However, you can also add a phone number easily by manually editing the trip item. Just open your trip, find the item, and click the edit button. Easy as pie.