harry potter - How did the Unspeakables know to change the records in the Hall of Prophecy?

Related: How do you listen to a prophecy without smashing it in Harry Potter?; How do the spheres with recorded prophecies appear in the Department of Mysteries?

We know that the contents of the prophecy concerning Harry were not common knowledge, and we know that neither Rookwood, who was an Unspeakable working in the Department of Mysteries before Voldemort's downfall, nor Bode, who was an Unspeakable placed under the Imperius Curse by the Death Eaters, could access the prophecy's contents, or else Voldemort would have been saved the trouble.

But at the end of Book 5, Dumbledore tells Harry this:

"The official record was relabeled after Voldemort’s attack on you as a child," said Dumbledore. "It seemed plain to the keeper of the Hall of Prophecy that Voldemort could only have tried to kill you because he knew you to be the one to whom Sibyll was referring."

So how did this "keeper" guy know to relabel the prophecy with Harry's initials, anyway, if he couldn't even get at its contents?

(Speculation is welcome if you have sound logical support.)

Answer

I suspect they simply listened to it

Dumbledore does indeed say that only the subjects of a prophecy can remove it from the shelf.

`And then you saw Rockwood, who worked in the Department of Mysteries before his arrest, telling Voldemort what we had known all along -that the prophecies held in the Ministry of Magic are heavily protected. Only the people to whom they refer can lift them from the shelves without suffering madness....'

—Harry Potter and the Order of the Phoenix

However, there is no reason to interpret this quote as implying that, from the very moment the prophecy is recorded, it is thus protected. The protections placed on prophecy records could easily be placed only after the Keeper has listened to them. Alternately, while the spells placed on the prophecies may automatically appear once the prophecies are recorded, it may be possible to remove them with enough effort. If Voldemort would have to stand in front of the prophecy for days, chanting, it would have been essentially impossible to remove the protections.

If so, why not kidnap the Keeper?

Why not target the Keeper, in either case? As someone who has listened to Harry's prophecy, there's a decent chance that they still remember the details, in which case Voldemort could simply kidnap them. It is possible that there is some additional security involved, such as Memory Charms cast on the Keeper. But I think there are two much simpler possibilities.

1. Voldemort wished to avoid drawing attention to himself. The disappearance of one who was surely a top Ministry official would do exactly the opposite, particularly if this happened after Bode attempted to steal the prophecy. Voldemort perhaps considered it, but considering the distinct possibility that the Keeper did not remember the details, why not wait a few months and tempt Harry Potter into removing it for him?


2. The Keeper was dead. Simple as that. The person who had listened to and relabeled Harry's prophecy was no more, and the only remaining record was on a shelf in the Hall of Prophecy. Of course, there would have been another Keeper, but they wouldn't know what the prophecy contained.