The TD needs to consider potential misinformation, unauthorised information and the fielded misbid regulations.
Misinformation
The explanation of 1NT was found to be correct, so there cannot be any adjustment for misinformation.
Unauthorised information
Unless, West showed any form of surprise when 1NT was not alerted, East does not have any unauthorised informaton.
West does have unauthorised information as at the point where he bid 1NT, he was expecting that bid to be alerted; the lack of alert woke him up to the fact that 1NT did not actually show both minors at all. However, it is hard to see how West's subsequent bidding and defence could have been affected by the UI, so no adjustment is appropriate in respect of UI.
Fielded misbid regulations
I believe this hand comes from England, where there are special regulations for "fielded misbids", which are treated similarly to "fielded psyches". The regulations are contained in the EBU Orange Book:
EBU Orange Book said:
6 B 3 A partnership’s actions on one board may be sufficient for the TD to find that it has an unauthorised understanding and the score will be adjusted in principle (eg 60% to the non-offending side and 30% to the offending side is normal in pairs). This is classified as a Red psyche.
6 B 4 A TD may find that whilst there is some evidence of an unauthorised understanding it is not sufficient, of itself, to justify an adjusted score. This is classified as an Amber psyche. In particular, if both partners psyche on the same hand, then a classification of at least Amber is likely to be justified.
6 B 5 In the majority of cases the TD will find nothing untoward and classify it as a Green psyche.
6 B 6 A TD may use evidence from a partnership’s actions on two or more boards to assess a partnership’s actions. Whilst a single instance may not provide sufficient evidence of an unauthorised understanding to warrant a score adjustment, a repetition reinforces the conclusion that an unauthorised understanding exists. In other words, if two psyches are classified as Amber, the classification of both automatically becomes Red, and the score on all such boards is adjusted accordingly.
6 B 7 A partnership’s actions following a deviation may provide evidence of an unauthorised understanding, but they are less likely to do so than after a psyche. As with psyches, deviations may be classified as Red, Amber or Green.
6 B 8 A partnership’s actions following a misbid may provide evidence of an unauthorised understanding, but they are less likely to do so because of the lack of intent to mislead. As with psyches, misbids may be classified as Red, Amber or Green.
East's explanation for the lack of double suggests that he would have made the same deduction with an unknown partner, so this does not provide any evidence of an undisclosed partnership agreement.
In this case, East's failure to double 4
♠ is hardly unreasonable, so I would classify the misbid as Green or possibly Amber.
Either way, the score should not be adjusted, as the regulations only permit an adjustment for Red misbids and psyches (unless this has happened before in this partnership, in which case 6B6 above tells us that we can adjust for repeated Amber misbids).
Butler scoring
N--E--S--W
1♥-P-1♠-1NT
4♠-All pass