The photo location is embedded into the image files on your camera, it's in something called EXIF data. I don't know if any native photo apps for either iOS or Android support editing that data but there are definitely 3rd party apps out there which will let you remove it. You can use one of those to remove the location embedded into the photo before uploading it.

Too bad!

I will never upload a photo again. Why hide your running start and goal location and the reveal it with a photo!‍♂

Another option would be to disable location data on your phone so it is never stored with the photos.

Android: https://www.howtogeek.com/303410/how-to-prevent-android-from-geotagging-photos-with-your-location/

iPhone: https://support.apple.com/guide/personal-safety/stop-and-remove-location-metadata-in-photos-ips0d7a5df82/web

No one can see the location of photos taken within a privacy zone except you. Also, all photos viewable on Strava have their metadata stripped, so downloading any photo from the Strava website will not reveal where it was originally taken.

I have just tested both of the above, and verified them to be true.

On Apple platforms, you can remove location information fairly easily (look for similar options on Android/Windows/Linux).

In the macOS Photos app, simply uncheck this option when exporting a photo:

On iOS, tap the Share button, then disable Location before saving the photos to your file system:

Now you can be certain that the photos do not include Location information before uploading to Strava, or any other social-media site. I believe that setting should persist until you change it back, at least on macOS.

If there are specific locations you never want to show in your photos, head on to Privacy Controls and simply add them to your privacy zones under Map Visibility: