I don't want any Apple Health data to show in Nutracheck anymore, how do I also remove previously shared data?

The easiest way is to delete and then reinstall the Nutracheck app (you will be able to sign back in as a registered member). When you delete the Nutracheck app, a pop-up will appear asking if you wish to remove all the 'Health' data. (You will not lose your Nutracheck diary data).