Update 5/31/16: The glitch has been addressed in iOS 9.3.1.
Apple released iOS 9.3 today, which contains lots of enhancements and fixes. One of these fixes solves an issue with the Calendar app (for those still not using the Outlook app), where it would send multiple responses for an invite.
The release notes of iOS 9.3 mention:
Resolves an issue for some Exchange users that caused Calendar to send multiple responses to the same invitation
The fix supposedly solves issue 1.15 from the “Current issues with Exchange ActiveSync and 3rd-party device” overview (KB2563324), “Meeting organizer receives multiple responses from attendee. The related KB article, KB3108212, also contains instructions on how to identify users experiencing this problem. Note that the problem has also been addressed server-side in Cumulative Update 1 for Exchange 2016.
It’s almost a law that, for every bug that is fixed, new ones are introduced. So, some organizations may therefor want to test and accept this iOS update before giving it the green light for their Exchange environment. To block a specific version of iOS from Exchange, consult the instructions here.