If you don't want directions to be shown on the traveler's map, do the following:
(Our product evolves quickly, and this video may not show the latest updates)
How To Manage Directions Display Settings
Go to Settings > Trips > Map
Find the "Show Directions" setting and choose whether you want the directions to be shown for each of your trips
Save your changes
How To Manage Directions Display Settings for a Specific Trip
Go to Trips
Select the trip for which you want to manage the directions display settings
Navigate to the "Share" step of that trip
In the trip's Settings section, under "Show Directions," select whether you want the directions to be displayed on the map
Save the trip