You will need the Edit Locations Admin/User permission to do this. Map data can be individually deleted or deleted in bulk. To delete them individually, once logged into the online account under the Map Data tab, you would select the point you want to delete. This will bring up an Edit Location box with a Delete button in the bottom left corner.  To bulk delete map data, you will select the Bulk Edit option on the Map Data tab. This will bring up a Bulk Edit Location box where you can choose what color and icon you want to have removed in the From section. To delete, leave the To section as Delete Orange. This is the default. Select submit when you are ready. It will ask you confirm before finally removing all the points of that color and icon.