(And please, nobody say "Cause Dumbedore asked them to")
We know one of the tasks of the Order after its re-creation was to keep safe a weapon Voldemort was after.
“What’s he after apart from followers?” Harry asked swiftly.
He thought he saw Sirius and Lupin exchange the most fleeting of looks before Sirius said, “Stuff he can only get by stealth.”
When Harry continued to look puzzled, Sirius said, “Like a weapon. Something he didn’t have last time.”
(Order of the Phoenix, Chapter 5, The Order of the Phoenix)
Sturgis Podmore was Imperiused while patrolling around the door behind which it was kept, and Arthur Weasley was attacked there by Nagini (or Voldemort in Nagini).
“Your father has been injured in the course of his work for the Order of the Phoenix,” said Dumbledore.
[...]
“The Ministry wouldn’t want everyone to know a dirty great serpent got —”
“Arthur!” said Mrs. Weasley warningly.
“— got — er — me,” Mr. Weasley said hastily,
[...]
“You were guarding it, weren’t you?” said George quietly. “The weapon? The thing You-Know-Who’s after?”
“George, be quiet!” snapped Mrs. Weasley.
“Anyway,” said Mr. Weasley in a raised voice...
(Order of the Phoenix, Chapter 22, St Mungo's Hospital)
-
“Sturgis Podmore,” said Hermione, breathlessly. “Arrested for trying to get through a door. Lucius Malfoy got him too. I bet he did it the day you saw him there, Harry. Sturgis had Moody’s Invisibility Cloak, right? So what if he was standing guard by the door, invisible, and Malfoy heard him move, or guessed he was there, or just did the Imperius Curse on the off chance that a guard was there? So when Sturgis next had an opportunity — probably when it was his turn on guard duty again — he tried to get into the department to steal the weapon for Voldemort"
(Order of the Phoenix, Chapter 26, Seen And Unforeseen)
We also learn later that the said weapon was the Prophecy about Voldemort and Harry.
Voldemort was after it, because he thought its end would tell him how to destroy Harry.
And so, since his return to his body, and particularly since your extraordinary escape from him last year, he has been determined to hear that prophecy in its entirety. This is the weapon he has been seeking so assiduously since his return: the knowledge of how to destroy you.
(Order of the Phoenix, Chapter 37, The Lost Prophecy)
But let's look at the content of the Prophecy, and what part he already knows of:
“THE ONE WITH THE POWER TO VANQUISH THE DARK LORD APPROACHES... BORN TO THOSE WHO HAVE THRICE DEFIED HIM, BORN AS THE SEVENTH MONTH DIES... AND THE DARK LORD WILL MARK HIM AS HIS EQUAL, BUT HE WILL HAVE POWER THE DARK LORD KNOWS NOT... AND EITHER MUST DIE AT THE HAND OF THE OTHER FOR NEITHER CAN LIVE WHILE THE OTHER SURVIVES... THE ONE WITH THE POWER TO VANQUISH THE DARK LORD WILL BE BORN AS THE SEVENTH MONTH DIES...”
(Order of the Phoenix, Chapter 37, The Lost Prophecy)
-
“He heard only the first part, the part foretelling the birth of a boy in July to parents who had thrice defied Voldemort."
(Order of the Phoenix, Chapter 37, The Lost Prophecy)
The bold parts are already known to Voldemort... and the rest of the prophecy does not really gives him valuable information:
- Mark him as his equal: OK, that's already done.
- He'll have a power the Dark Lord knows not: Yep, that's love. But since Voldemort does not know of it, he won't be able to understand this sentence. He will imagine another power, but that won't help him (and he probably already guessed this while planning to kill baby Harry).
- Either must die at the hand of the other...: Alright, so Voldemort should go and kill Harry then! Oh, but he kind of already wanted to anyway, didn't he?
Was preventing Voldemort from hearing the end of the Prophecy worth all the trouble and the risks (one member of the Order lost for 6 months to Azkaban, another heavily wounded and happy not to be dead...)? Why did they bother to do so?