It would never occur to me to challenge a NC once it has been committed to paper and the audit report is issued. If nothing else it would make the auditor look bad to their management if you are right, which would not be a good thing to do for the future of the relationship. Especially over a minor.
We have successfully challenged a number of NCs at the point of origin or at the daily debrief level. One strategy that works is to put in place a system that treats observations and NCs exactly the same (i.e. observations get documented corrective action plans, verification of corrective action, follow-up, etc.). If a NC is not entirely clear-cut you can then petition the auditor to make it an observation, while gently reminding them that under your system it will still be treated the same as a NC. You should of course be ready to explain why you don't believe it is a NC, and back it up with good objective evidence.
Of course, that means you still need to do corrective action, but an observation sounds better than a NC and the auditor won't need to review your corrective action.
Some auditors won't write observations. If you get one of those, you're out of luck.
I would never use that approach on a clear NC. If it's a clean hit, take it standing up and don't argue. It's the fuzzy ones that auditors may be willing to deal on.
Ed Gibbs