I have read or listened to Harry Potter books many times, but I have never noticed this. In the fourth book
Harry Potter and the Goblet of Fire Hermione starts S.P.E.W. :
“What’s in the box?” he asked, pointing at it.
“Funny you should ask,” said Hermione, with a nasty look at Ron. She took off the lid and showed them the contents. Inside were about fifty badges, all of different colors, but all bearing the same letters: S. P. E.W.
“Spew?” said Harry, picking up a badge and looking at it. “What’s this about?”
“Not spew,” said Hermione impatiently. “It’s S-P-E-W. Stands for the Society for the Promotion of Elfish Welfare.”
“Never heard of it,” said Ron.
“Well, of course you haven’t,” said Hermione briskly, “I’ve only just started it.”
Then in the next book
Harry Potter and the Order of the Phoenix Hermione decides to start knitting woolly hats for the house elves, I assume in hope of freeing them:
“They’re hats for house-elves,” she said briskly, now stuffing her books back into her bag. “I did them over the summer. I’m a really slow knitter without magic, but now I’m back at school I should be able to make lots more."
“You’re leaving out hats for the house-elves?” said Ron slowly. “And you’re covering them up with rubbish first?”
“Yes,” said Hermione defiantly, swinging her bag onto her back.
“That’s not on,” said Ron angrily. “You’re trying to trick them into picking up the hats. You’re setting them free when they might not want to be free.”
“Of course they want to be free!” said Hermione at once, though her face was turning pink. “Don’t you dare touch those hats, Ron!”
I think her intentions are clear - she thinks she might free them if they pick (accidentally or intentionally) the hats (which are a bit of clothes). Her plan seems good, considering she probably learned about house elves from Harry's knowledge about Dobby (of course she might have read loads of books about house elves too):
"But why don't you leave? Escape?"
"A house-elf must be set free, sir. And the family will never set Dobby free ... Dobby will serve the family until he dies, sir ...."
"Why d'you wear that thing, Dobby?" he asked curiously.
"This, sir?" said Dobby, plucking at the pillowcase. "'Tis a mark of the house-elf's enslavement, sir. Dobby can only be freed if his masters present him with clothes, sir. The family is careful not to pass Dobby even a sock, sir, for then he would be free to leave their house forever."
"What's that?" spat Mr. Malfoy. "What did you say?"
"Got a sock," said Dobby in disbelief. "Master threw it, and Dobby caught it, and Dobby -- Dobby is free. "
But I see a gap in her plan. A house elf is freed if his/hers master presents him/her with a piece of clothes (e.g. a sock). Although Dobby later says:
"Harry Potter freed Dobby!" said the elf shrilly, gazing up at Harry, moonlight from the nearest window reflected in his orb-like eyes.
The piece of clothes still has to be given by the master and not anybody else -- if not Harry could give Dobby a piece of clothes and free him (which does not obviously make a sense).
But from this piece:
“And then Dobby had the idea. Harry Potter, sir! ‘Why doesn’t Dobby and Winky find work together?’ Dobby says. ‘Where is there enough work for two house elves?’ says Winky. And Dobby thinks, and it comes to him, sir! Hogwarts! So Dobby and Winky came to see Professor Dumbledore, sir, and Professor Dumbledore took us on!”
I assume, that Hogwart's house elves master is Dumbledore himself. So he is the only one, who can set them free.
Together Isn't Hermione's plan unable to work from the beginning? No matter what is the answer it does not work either way:
“Winky is still drinking lots, sir,” he said sadly, his enormous round green eyes, large as tennis balls, downcast. “She still does not care for clothes, Harry Potter. Nor do the other house-elves. None of them will clean Gryffindor Tower any more, not with the hats and socks hidden everywhere, they finds them insulting, sir. Dobby does it all himself, sir, but Dobby does not mind, sir, for he always hopes to meet Harry Potter and tonight, sir, he has got his wish!”
Note I have taken the texts from online available sources and decided not to add citations. Also I have decided to add so much texts since it provides you with full context and it does not hurt to read it through.