Should the app handle this or should I just throw my arms in the air and not commit the whole transaction?

If you API gives you a list of invalid items it's up to your business rules to decide whether or not these items are important for the app to remain consistent.

Sounds reasonable, its users -> messages, if message references foo@bar.quax user, thats a fk violation, would you rather see something as [Invalid user] at the message or not see the message at all?

I guess, as a user I'd rather prefer to see all my messages. Even if the sender wasn't identified.

yea, thanks