How do I delete the data from the period tracking app

Settings -> Privacy -> Health -> Cycle Tracking -> scroll to the bottom and click "Delete All Data from Cycle Tracking". Hope this helps! (For the most recent IOS)

Additionally, you may need to also delete the individual information from the health app as well as the cycle tracking app. Similar to the process above: Settings -> Privacy -> Health -> Health -> Click on all categories related to cycle tracking and click "Edit" in the top right and then "Delete All". You may need to do this for all cycle related data you've saved such as contraception, any symptoms you've saved, and sexual activity.

ouch and hold the Cycle Tracking app until the app icon jiggles. If the app doesn't jiggle, make sure that you're not pressing too hard. Tap the delete button , then tap Delete App.

Track your period with Cycle Tracking - Apple Support

I do not believe this removes the data from apple's servers, only on the device. For those looking for privacy under the new abortion restrictions, this solution may not protect you.