Can I somehow delete unwanted track points on a recorded track?

I don't think you can do this within the Explore system. Your best bet is to export the track (from the Map tab) as a .gpx. Then edit the .gpx (with something like Notepad) to remove the points you do not want. Probably based on the timestamp. Alternatively, you can do this with your favorite mapping/track management software. Probably even with BaseCamp if that's your tool of choice.

You can then upload the result as a new track if you want it in the Explore system.

Hi, I have exactly the same problem.  Forgot to stop tracking after a 6 day hike and I now have 200 miles of car journey saved too!  Did you manage to resolve yours? 

This seems like a feature gap.  Deleting unwanted points is probably something many customers would want