As we know, in Harry Potter and the Deathly Hallows Part 1, Antonin Dolohov and Thorfinn Rowle attacked Harry Potter, Hermione Granger, and Ron Weasley at Tottenham Court Road, but they were defeated and their memory was wiped by Memory Charm.

According to this,

Remus Lupin

was killed by Antonin Dolohov during the Battle of Hogwarts - so how did he get back his memory and skills?

According to Pottermore, Obliviate is a charm whose purpose is:

To erase, or modify the memory of another

With the effect being:

The recipent will lose a portion (or all) of their memory, depending on how strong the spell is

Since it was Hermione's first time casting the charm, and her intention was to just erase Dolohov's memory of seeing Harry, she probably didn't erase Dolohov's entire memory (like the backfiring charm did to Gilderoy Lockhart.

In fact, in J.K. Rowling's writing on Pottermore about "Illness and Disability", she implies that a properly cast Obliviate charm doesn't create "permanent amnesia" when she states:

[...] the consequences of curses or backfiring magic could be serious, permanent or life-threatening. This is the reason that Gilderoy Lockhart, victim of his own mangled Memory Charm, has permanent amnesia.

Memory Charms don’t always erase everything.

Though it is possible for Obliviate to erase all of someone’s memories, it’s more often used to erase the memories of a specific incident. It’s often used on Muggles who witness magic to erase their memories of it, and they only forget that specific incident. When the site manager of the campsite where the Quidditch World Cup has his memory modified, he remembers he’s the site manager and continues doing his job.

“Obliviate!’ he said sharply, pointing his wand at Mr Roberts.

Instantly, Mr Roberts’s eyes slid out of focus, his brows unknitted and a look of dreamy unconcern fell over his face. Harry recognised the symptoms of one who had just had his memory modified.

‘A map of the campsite for you,’ Mr Roberts said placidly to Mr Weasley. ‘And your change.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 7 (Bagman and Crouch)}}

After his memory of the Death Eaters attacking is erased, Mr. Weasley, who loves Muggles so would care about what happens to them, assures Harry he’ll be all right, he’s just a bit dazed because that’s a temporary side effect of having his memory modified and it was a big thing that needed to be erased from his memory.

“He used magic to pack up the tents, and they left the campsite as quickly as possible, passing Mr Roberts at the door of his cottage. Mr Roberts had a strange, dazed look about him, and he waved them off with a vague ‘Merry Christmas’.

‘He’ll be all right,’ said Mr Weasley quietly, as they marched off onto the moor. ‘Sometimes, when a person’s memory’s modified, it makes them a bit disorientated for a while … and that was a big thing they had to make him forget.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 10 (Mayhem at the Ministry)}}

Mr. Roberts only forgot his encounters with magic, not everything else. It’s likely the same sort of thing happened to Dolohov and the other Death Eaters. Hermione likely just erased the Death Eaters’ memories of seeing them, not all of their memories, so they’d still remember that they were Death Eaters when they ‘woke up’.

It seems pretty clear from the book that they deliberately only erased the memory of the altercation and not the Death Eaters' other memories. Consider the following dialogue from chapter Nine:

"What are we going to do with them?" Ron whispered to Harry through the dark; then, even more quietly, "Kill them? They’d kill us. They had a good go just now."

Hermione shuddered and took a step backward. Harry shook his head. "We just need to wipe their memories," said Harry. "It’s better like that, it’ll throw them off the scent. If we killed them it’d be obvious we were here."

"You’re the boss," said Ron, sounding profoundly relieved. "But I’ve never down a Memory Charm."

"Nor have I," said Hermione, "but I know the theory."

She took a deep, calming breath, then pointed her wand at Dolohov’s forehead and said, "Obliviate."

At once, Dolohov’s eyes became unfocused and dreamy.

"Brilliant!" said Harry, clapping her on the back. "Take care of the other one and the waitress while Ron and I clear up."

"Clear up?" said Ron, looking around at the partly destroyed café. "Why?"

"Don’t you think they might wonder what’s happened if they wake up and find themselves in a place that looks like it’s just been bombed?"

"Oh right, yeah..."

As we can see from this exchange, what they wanted to do was to make sure that no one would realize that anything had occurred, and most importantly that no one would realize that they had been there. They chose not to kill the Death Eaters for this reason — two dead Death Eaters in a café is awfully suspicious and would immediately inform Voldemort's side that there had been some kind of run-in with opposing forces.

Entirely wiping their memories (to the point that they would be unable to perform magic) would be just as bad of an option. If two Death Eaters are discovered totally out of their minds that also immediately points to an altercation with the opposition. Therefore, all they did was remove the memories of the incident itself so that the Death Eaters could go on their merry way without anyone's suspicions being raised.

In any case, the plan didn't work so well, as we see later (same chapter) that Voldemort found out that the Death Eaters had been with Harry Potter:

"More, Rowle, or shall we end it and feed you to Nagini? Lord Voldemort is not sure that he will forgive this time.... You called me back for this, to tell me that Harry Potter has escaped again? Draco, give Rowle another taste of our displeasure.... Do it, or feel my wrath yourself!"