You can update your screenshots easily in Google Play by sending us your new screenshots.
For Apple however, updating screenshots requires that you re-submit your app.
Here is the official line from Apple:
App screenshots will be locked in iTunes Connect once your app has been approved. New screenshots may be uploaded when you submit a binary for an update to an existing app or a new app.
We do not support updating a binary for simply updating screen shots. Periodically we update your app with the latest fixes and improvements, so you will get the opportunity to update your screenshots then.