Sometimes a trip just doesn't work out and you want to get rid of it. Like Archived caches, there is no permanent delete of a trip. What you can do is Cancel the trip. The "Cancel trip" action is in the Edit menu for the trip.
All participants will receive an alert via e-mail, and the trip will no longer appear in any lists. You will still be able to find the trip by searching, and any links to it will still work. This action cannot be undone.