Thank you MartyBartfast for taking the time to reply. Unfortunately, the three parts to your answer all missed the mark.
>> The first 'straight line' is because when you turn the GPS on it registers it's last known location, then when it figures out where it is it draws a tack from the last known location to where you are now.
The problem with that theory is that I was never at the bottom of the ravine. The coast range at the California / Oregon border consists typically of near vertical slopes from ridge top to ravine. One lane dirt roads are cut into the slope. I was parked on such a dirt road for the night and turned off the GPS. Turned it back on when I continued the drive. Now I've got a track segment that shows that I was down in the ravine, at nearly a right angle to the road (I have a topo map loaded in the GPS and you should see the topo lines one of the tracks crosses). I think I'd have remembered the climb if I'd been down there.
>> The .gpx file is a text xml file which you can edit with a text editor and remove the first track waypoint.
The waypoint file contains hundreds of waypoints, and somewhere in all those are a few that I want to delete. Also, I don't really want to submit the entire track, only the portion of the track once I hit BLM (Bureau of Land Management - outback) roads. I don't want to manually plot each of these hundreds of waypoints. I want a program that plots the entire list on a map. I envision a simple iterative process. I use a program that shows my waypoint file's contents superimposed on an OpenStreetMap map. Meanwhile, I've got the file containing the list open in a text editor. I delete some waypoints in the text editor and refresh the map program. If I like the results, I continue on deleting more waypoints. If I find I've deleted waypoints I didn't want to delete, I undo (The Geany text editor I use allows undo past save).
>>Once you've uploaded the track to OpenStreetMap you can then edit the track on there.
You are answering a question I didn't ask. I didn't ask how to use OpenStreetMap to edit my waypoints, I asked how to edit my waypoints locally.
Again, I appreciate you're attempt to help, but, unfortunately, nothing you wrote actually did help.