Here's the scenario:

We had a check present twice in our inclearing file yesterday. Both items clearly deposited via mobile deposit. We returned the second presentment as Duplicate. The check was then taken to one our branches and cashed in the afternoon.

Here's the question:

Can we return the first inclearing check and pay the cashed check?

you can

Curiosity question -- was there a restrictive indorsement on the check indicating it had been mobile-deposited when your teller cashed it? If so, you've got some training to do. You might also check to see if your teller system should have alerted the teller that the check had already been presented.

No, neither of the mobile deposited checks had a restrictive endorsement on them. Just the payee's name.
The teller checked in every system they should have. The only thing they didn't do was to look at the memo posted items closely enough.