This happens to me too. My solution is to unsync and resync with the server:
- go to Settings / Main, Contacts, Callendars
- in the Accounts group, go to the appropriate account (for me, it always happens with MS Exchange)
- Switch off Calendars (events will not be synced from this server any more)
- You will be asked whether you are sure, because it will delete all the events that are currently synced from this server. Don't worry, they will remain on the server. They will be just deleted from your phone, including the stuck invitation.
- Wait a moment
- Switch on Calendars again
- Now you can go to Calendar app. Events from that server will be missing, but will be being downloaded again. After a short while, all the events will be back in your calendar, but the stuck invitation will be cleared.
It has happend to me several times since upgrading to iOS 7.0, say once per month, and it's shame that it was not fixed by iOS 7.1.
I have the exact same issue with the same setup - the only difference is that my wife and I both have the iPhone 4S. Unfortunately I don't have a solution. Anyone else seeing this?