You can delete your distance entries via both the website and app. Please note that synced entries (eg. from Fitbit, Apple Health) cannot be deleted - contact support if you need assistance with this.
On the Website
If you open the Dashboard on the challenge website, you will see you activity feed. You can also view this on your Daily Activity page.
If you wish to delete an activity, click on the delete button beside activity. You'll be asked to confirm that you really wish to delete it before continuing.
On the App
You can delete entries from the app either via the Dashboard activity feed, the daily activity feed, or your Profile activity feed.
Just tap on the delete button beside one of your own activity entries and tap "Delete" to confirm.