The rules clearly state on the back page that defeating the challenge (averting the threat) you discard the card without further consequences. However inside the rules by the threat symbol it says "before discarding a threat card carry out its instructions below the threat symbol."
The latter is when you have to discard a threat because you finished a scenario before averting the threat, the way I read it.
So there are really two ways of discarding a threat:
1) averting a threat
- if you pass the check, discard the threat without any further effect
- if you fail the check, the threat stays in play
2) finishing a scenario
- carry out the instructions, then discard