You can archive trips you no longer need to clean up your My Trips menu.

Manage archived trips in your account settings, "Trips" page. (You can get there from the bottom of the My Trips menu.)

Find the trip you want to delete, and click the "Archive" button next to it. If you change your mind later, all your archived trips are listed at the bottom of that page. You can always click "Restore" in that list to undelete the trip and bring it back to your My Trips menu.