Facts:
1. The auction was (1
♣)-2NT-(P)-3NT-AP, making North the declarer and putting East on opening lead.
2. Before leading, East asked South the meaning of 2NT.
3. The explanation given was "Natural, 2NT opening strength".
4. East looked at North's convention card, which said 2NT showed the two lower unbid.
5. The two lower unbid suits are diamonds and hearts.
6. North has diamonds and clubs.
Procedural points:
1. When North hears, during the Clarification period, South's explanation of the meaning of 2NT, he is required, if he disagrees with the explanation, to 1) call the TD, 2) explain, in the TD's presence, the nature of the disagreement.
2. When East, after hearing South's explanation, sees that North's system card does not match that explanation, he should call the director and ask the director to resolve the discrepancy.
3. Technically, North should not respond to East's question about North's own bid unless and until instructed to do so by the director, so when the question is asked, North should call the director.
4. The director should investigate and determine, based on the preponderance of the evidence, what the actual agreement is. Without talking to NS, I'm not going to speculate.
It looks to me like North is going to come to ten tricks whatever the opening lead is. So there is no damage, even if there was an infraction. No damage, no score adjustment. Now...
Questions from the OP:
1. Adjust, or no?
2. Does the answer depend on what N was thinking when he bid 2NT?
3. If N thought 2NT showed the minors, does it matter how or when he became aware his card was marked "two lower unbid"?
1. No. See above.
2. No.
3. Not in this case. If 2NT shows the two lower unbid, North misbid. If 2NT is natural, North misbid. North is not required to tell his opponents that he misbid.
A further question: did South "field" North's misbid? My answer: no.
Whatever the TD decides the agreement actually is, he should ensure that NS amend their system card(s) so the that explanation on both cards is the same, and matches their agreement (even if they decide they want a different agreement to what the TD decides
was the agreement). If, after a reasonable time (say, by the beginning of the second round following this one), this has not been done, the TD should issue a PP.
Further thoughts:
1. There are four possible agreements here:
a) 2NT is natural
b) 2NT is both minors
c) 2NT is the two lower unbid suits
d) they actually have no agreement.
and a fifth: they have some other agreement, but I suspect the likelihood of that is pretty small.
There is evidence (North's card) that the agreement is c). There is evidence (North's bid) that the agreement is b). There is evidence (statements from both North and South, and the fact that South's system card was blank in this area) that the agreement is a). The fact that South's card was blank might also be evidence that the "agreement" is d). The preponderance of the evidence here seems to indicate that the agreement is a), but I would want to investigate further.
The OP does not state his bridge jurisdiction, but he appears to be in the US, so ACBL rules would apply.
Please folks, when you post a question here, let us know the jurisdiction! It may make a difference. Under ACBL rules, a natural 2NT in this auction requires an alert, so one of the questions I'd be asking is why South did not alert it. The fact he did not is evidence that perhaps it is not the case that their agreement is natural.
Note that in the ACBL, weighted scores do not apply, so if we
were going to adjust, we would use Law 12C1{e}, not Law 12C1{c}, and the OS would get "the most unfavorable result that was at all probable had the irregularity not occurred", and the NOS would get "the most favorable result that was likely had the irregularity not occurred".