Daniel Scavone, in 'Deconstructing the "Debunking" of the Shroud', brings all the evidence we have to the table, as it were. It consists of a number of letters, which seem to indicate a rather petty spat between two figures of some standing, each attempting to draw crowds, and revenue, from the other. Pope Clement is caught between these, and awkwardly attempts to placate both. De Charny may show his relic as long as he does not declare it the authentic burial shroud, and d'Arcis must stop bickering about it. This instruction precedes the famous 'memorandum' and may have been the reason why d'Arcis did not pursue it. Nevertheless he did write it, made copies, and asked for amendments. There is no reason to suppose he did not believe that what he wrote was true, and it may be that the artist was indeed known, at least to Bishop Henri if not to d'Arcis. If, however, it was created as a prop for something more important liturgically than a mere relic, namely an Easter reenactment, then there is no reason why it, and the priory containing it should not have been welcomed. In the 30 years between its appearance in about 1355 and its display in about 1385, something may have changed. Even if it is one among many Quem Quaeritis shrouds now lost, it is a superb creation far outweighing any contemporary depiction of Christ in design and (artistic) execution. Maybe people began to believe that this was the real thing (and who was de Charny to deny them their credulity) and maybe someone claimed it had caused a miracle, further attesting to its authenticity.
Is there any evidence for this? None whatever. It is merely a reasonable explanation as to why d"Arcis might have written his memorandum, believing it to be true, but not sent it. Without knowing rather more than I do about these Bishops, I think there is little that I can add that does not push speculation into fantasy.