You can export the tcx and gpx files from the details page for each activity. If you want to do this for many activities, you should consider scripting it. Additionally, you might be able to use Tapiriik to export your activities to a dropbox account where you cold harvest them. Another option would be for you to maintain a backup of the .fit/tcx/gpx files generated by your device, before they are uploaded to Garmin Connect.
