I wouldn't bother. They could, but their not suppose to. Anyone could take a screenshot and edit it to say whatever they want. I've never had a FP just disappear or any troubles. So I would just stick with planning on them staying put and not worrying about screenshots.
Only reason I take screenshots is so you don't have to wait for the app to load and use battery life to remember what fast passes and times. Easier to just check out the pictures