How do I delete a Route on the iPhone?

Routes on the iPhone are stored under the Routes section. From the Menu page, tap 'Favorites' under the 'Routes' section. Next, tap 'Favorites' or 'Recents' at the bottom and then either use the 'Edit' button or swipe from right to left across the route you want to delete and select 'Delete.' 

Alternatively, if you want delete the current route that is in your NavLog, then from the Maps page, tap on the 'NavLog' button and then tap the x at the right end of the Search box. Now you can enter a new Route.