I am trying to delete segments so they do not appear in my Garmin Connect app.
On the web, I go to completed segments however there is no option to delete these?
How do I go about deleting these so I see only selected segments in the app.
You can only delete segments that you created. You cannot delete segments created by other users. The only possibility is in the case where you do not wish to see any segments at all - in that case you can opt out completely.
