As promised, Microsoft has worked to disable their online website used for sharing in their photo apps.
With the latest update to the Lumia Refocus app the app now also no longer offers to upload your image to the Refocus website.
The app still works to create refocusable images, but with no clear way to share these.
Interestingly the .NAR files the app produce (which end up in your camera roll) appear to be compressed archives with around 8 images and some meta data, so in theory some-one could create a 3rd party app to do something useful with these images.
If you are interested in disabling your sharing early (officially the website is being removed on the 30th October) you can find the app in the Windows Store here.