Although what Richard says is true I want to answer your question about why the Death Eaters could seemingly see through it (actually even Dumbledore didn't he just inferred it as he knew who owned the cloak and he also knew that Harry got along well with Hagrid). What you must understand is in that same scene the Cloak of Invisibility isn't even over them. What happened is this: Mr. Lovegood was in his folly sure that Hermione was wrong and that the Erumpent horn wasn't dangerous because it was from a Crumpled Snorkack. This would be to the destruction of his house. He just told the trio that he would have to turn Harry in:
'The Quibbler's going for a new angle, then?' Harry asked coldly,
his mind working very fast. 'Is that what you were doing when
you went into the garden, Mr. Lovegood? Sending an owl to the
Xenophilius licked his lips.
'They took my Luna,' he whispered. 'Because of what I've been
writing. They took my Luna and I don't know where she is, what
they've done to her. But they might give her back to me if I — if
'Hand over Harry?' Hermione finished for him.
'No deal,' said Ron flatly. 'Get out of the way, we're leaving.'
Xenophilius looked ghastly, a century old, his lips drawn back
into a dreadful leer.
'They will be here at any moment. I must save Luna. I cannot
lose Luna. You must not leave.'
Once the Death Eaters arrived though he decided to try and stun the trio. However, they got out of the way just in time. This blew up the house just as the Death Eaters arrived:
'HARRY!' Hermione screamed.
Figures on broomsticks were flying past the windows. As the three of them looked away from him, Xenophilius drew his wand. Harry realised their mistake just in time: He launched himself sideways, shoving Ron and Hermione out of harm's way as Xenophilius's Stunning Spell soared across the room and hit the Erumpent horn.
This blew the house apart and the Death Eaters thought it was an ambush and they also seemed to have cast Crucio on him:
'Didn't I tell you there was no need to hurry, Travers?' said a rough voice. 'Didn't I tell you this nutter was just raving as usual?' There was a bang and a scream of pain from Xenophilius.
'No . . . no . . . upstairs . . . Potter!'
'I told you last week, Lovegood, we weren't coming back for anything less than some solid information! Remember last week? When
you wanted to swap your daughter for that stupid bleeding headdress? And the week before' — another bang, another squeal — 'when you thought we'd give her back if you offered us proof there are Crumple' — bang — 'Headed' — bang — 'Snorkacks?'
What happens next shows that the trio weren't under the Cloak at the time:
'You lying piece of filth,' shouted the wizard named Selwyn.
'You've never seen Potter in your life, have you? Thought you'd
lure us here to kill us, did you? And you think you'll get your girl
back like this?'
'I swear . . . I swear . . . Potter's upstairs!'
'Homenum revelio,' said the voice at the foot of the stairs.
Harry heard Hermione gasp, and he had the odd sensation that
something was swooping low over him, immersing his body in its
'There's someone up there all right, Selwyn,' said the second
'It's Potter, I tell you, it's Potter!' sobbed Xenophilius. 'Please . . .
please . . . give me Luna, just let me have Luna. . . .'
'You can have your little girl, Lovegood,' said Selwyn, 'if you
get up those stairs and bring me down Harry Potter. But if this is
a plot, if it's a trick, if you've got an accomplice waiting up there to
ambush us, we'll see if we can spare a bit of your daughter for you
Hermione as usual did the logical thing, remembering that Ron wasn't supposed to be with them but actually ill, not on the run:
'All right,' breathed Hermione, as the broken printing press
blocking the top of the stairs began to tremble; Xenophilius was
feet away from them. She was still white with dust. 'Do you trust
'Okay then,' Hermione whispered, 'give me the Invisibility
Cloak. Ron, you're going to put it on.'
'Me? But Harry —'
'Please, Ron! Harry, hold on tight to my hand, Ron, grab my
Harry held out his left hand. Ron vanished beneath the Cloak.
The printing press blocking the stairs was vibrating: Xenophilius
was trying to shift it using a Hover Charm. Harry did not know
what Hermione was waiting for.
'Hold tight,' she whispered. 'Hold tight . . . any second . . .'
Xenophilius's paper-white face appeared over the top of the
After covering Ron with the Cloak she wipes Lovegood's memory and then shows the Death Eaters that in fact Harry and Hermione were indeed there - but they then Apparated:
'Obliviate!' cried Hermione, pointing her wand first into his
face, then at the floor beneath them. 'Deprimo!'
At this point the Death Eaters didn't see Ron but they did see Harry and Hermione. In this way they would know that Lovegood wasn't trying to trick them and it also didn't give away Ron's cover.
So in this case the Cloak was entirely irrelevant as they weren't under it.
But as it happens Dumbledore cast silently the same spell in the Chamber of Secrets but it's not impervious to that spell; it cannot be summoned but the human revealing spell doesn't actually target the Cloak itself; instead it targets the area. Even so Dumbledore wandlessly and silently immobilises Harry in Half-Blood Prince at the top of the Astronomy Tower but the target is Harry and not the Cloak itself.