Once you have completed a search of flights for a traveler, you will see that flight option in the Flight Card in your Project Page, as seen below:
The traveler's flight has not been confirmed yet, it is just sitting in your project waiting to move to the next step. If you wish to remove this flight and find another options you will want to click the down arrow to the right of the "Book For" button which will show you the flight details.
Once there, you will want to click "Change Flight," which will take you to the Search screen and will initiate another search.
You have two choices from here:
If you wish to remove the Flight Card altogether for the Traveler, you can click the "Delete Flight" button at the top right, and this will delete the flight and return you to an empty state for that Traveler, where you can change the flight parameters and search again or even delete the traveler from the project.
You can update the flight parameters at the top of the screen and click Search Flight from this screen.
Clicking Search will bring up an updated list of flight options, and you can choose your new flight, which will update the Project Page.