Fixing the Apple Health <> Strava integration is planned for 2017.
Currently, after connecting Strava and Apple Health, some Strava activity data is appearing twice in Apple Health. Troubleshooting this problems is difficult and hard to reliably reproduce. In most cases the duplicate entries reappear again at some point.
In the meantime, below are steps that may temporarily resolve the duplicates:
In Health, turn off all sources for each of the data types (Active Calories, Cycling Distance, Walking + Running Distance, Workouts).
Close the Health app and the Strava app.
Start Health app again and turn all Strava sources back on, including the Workouts option.
Start up Strava, go to the "You" feed and pull down to refresh. Then scroll down through that feed to view past activities which allows that data to be pulled from the Strava servers and passed into the Health app.
If that doesn't work, you may have to delete and reinstall the Strava app. You won't lose any data if you do this because it's all stored on the Strava servers (and when prompted to remove Health related data, say yes). To get entries back in to Health app, go to settings after reinstalling Strava and enable Health sharing.
- Editing the activity after saving it will sometimes trigger the duplicate activity. This includes changing your gear and cropping the activity.
- Uploading a manual activity to Strava and viewing the feed can clear out some of the duplications in Health.