If your watch was hallucinating about stair climbing it will have stored the phantom climbs in iCloud and your iPhone as part of your Health and Activity data. This will be retrieved after erasing and re-pairing the watch. It would even be transferred to a new iPhone or Apple Watch.
The underlying data can be viewed in your iPhone's Health app, and if you have time to spare you could edit by deleting any events you think were in error. Health app / Activity / Flights Climbed / (scroll down to Show All Data). At this stage you have to find the events you wish to delete, and swipe left to action the delete. If there are hundreds it might take some time!