In the new Trips experience, Trips can be archived or deleted, but Itineraries and Proposals can only be Archived within the Trip they are on. Let's go over how!
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To archive or delete a Trip, first click on that trip, and then click on the three dots in the top right-hand corner.

The option to Archive will appear!

To delete that Trip and all Itineraries/Proposals on that Trip, the Trip will first have to be archived, and then the delete option will appear in the same place:

Click on the Itinerary/Proposal you'd like to archive.

Click on the Box icon on the far right of your screen, and the Itinerary/Proposal will be archived.