The Deathly Hallows aren’t well-known.
The Death Eaters wouldn’t be likely to suspect Harry of having a Deathly Hallow, because it’s unlikely that the Death Eaters would even know about the Deathly Hallows to begin with. Xenophilius Lovegood isn’t surprised at all when Harry, Ron, and Hermione haven’t heard of them, because very few wizards believe in their existence.
“The Deathly Hallows?’
‘That’s right,’ said Xenophilius. ‘You haven’t heard of them? I’m not surprised. Very, very few wizards believe.”
- Harry Potter and the Deathly Hallows, Chapter 21 (The Tale of the Three Brothers)
The Death Eaters also likely wouldn’t have heard about the Deathly Hallows on their own, and the Dark Lord kept his search for the Elder Wand (not the Deathly Hallows - he may not have known about them himself and wouldn’t care if he did) to himself, so they wouldn’t know from the Dark Lord’s information either.
“But to be sure, to be utterly sure, he must return to each of his hiding places, he must redouble protection around each of his Horcruxes … a job, like the quest for the Elder Wand, that he must undertake alone …”
- Harry Potter and the Deathly Hallows, Chapter 27 (The Final Hiding Place)
Therefore, it’s unlikely that the Death Eaters even knew about the Deathly Hallows to be able to suspect Harry’s invisibility cloak of being one.
There are other invisibility cloaks.
It also wouldn’t seem unusual to the Death Eaters that Harry would have an invisibility cloak. Invisibility cloaks are rare, but their existence is well-known in the wizarding world - Ron is able to recognize one in his first year.
“Harry picked the shining, silvery cloth off the floor. It was strange to the touch, like water woven into material.
‘It’s an Invisibility Cloak,’ said Ron, a look of awe on his face. ‘I’m sure it is – try it on.”
- Harry Potter and the Philosopher's Stone, Chapter 12 (The Mirror of Erised)
Other wizards have owned invisibility cloaks - Moody had two.
“Found it last night when I was looking for my spare Invisibility Cloak, seeing as Podmore hasn’t had the manners to return my best one … thought people might like to see it.”
- Harry Potter and the Order of the Phoenix, Chapter 9 (The Woes of Mrs Weasley)
Invisibility cloaks are also mentioned in “Fantastic Beasts and Where to Find Them”, a very common wizarding book that every Hogwarts student has read.
“Demiguise pelts are highly valued as the hair may be spun into Invisibility Cloaks.”
- Fantastic Beasts and Where to Find Them
It wouldn’t seem unusual to the Death Eaters that Harry Potter, the heavily favored “Boy Who Lived” would have an invisibility cloak, since he’s considered important to keep hidden.
Harry’s cloak isn’t obviously unique.
In addition, there’s nothing so obviously special about Harry’s invisibility cloak that the Death Eaters would become suspicious of it with the limited information and interaction they had with it. Though he knew of their existence, to figure out if it was a Deathly Hallow, Dumbledore borrowed it from James Potter and examined it.
“You have guessed, I know, why the Cloak was in my possession on the night your parents died. James had showed it to me just a few days previously. It explained much of his undetected wrongdoing at school! I could hardly believe what I was seeing. I asked to borrow it, to examine it. I had long since given up my dream of uniting the Hallows, but I could not resist, could not help taking a closer look … It was a Cloak the likes of which I had never seen, immensely old, perfect in every respect … and then your father died, and I had two Hallows at last, all to myself!”
- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)
Dumbledore, who knew of the Hallows, explains in his notes on “The Tale of the Three Brothers” that though the cloak described in the legend is uniquely durable, true invisibility cloaks do exist.
“True invisibility cloaks, though rare, exist in this world of ours; however, the story makes it clear that Deaths Cloak is of a uniquely durable nature.22”
- The Tales of Beedle the Bard
With only the knowledge that Harry has an invisibility cloak and very limited interaction with it, and without knowing of the Deathly Hallows, the Death Eaters would have no reason to suspect that Harry’s own is any particularly unique type of invisibility cloak.