They gave them back, stripped of their armour but unharmed, like all other Greeks did.

In their treatment of the enemy dead, the pious Spartans adhered to the practices that were shared among all Greek communities - what some sources proudly call "the customs of the Greeks". These were based on the sacred principle that all men deserved a proper burial, and that it was undignified and unhealthy for corpses to be left in the field to rot. For personal, social, and religious reasons, the dead had to be either buried or cremated with all proper ritual, allowing their next of kin to mourn and the community to commemorate those who died. Since both sides were anxious to make sure that their fallen warriors would be taken care of, the Greeks (probably in the early 5th century BC) introduced a particular custom that is recorded in formulaic phrases at the end of nearly every battle description from the Classical period.

This custom was pretty straightforward. At the end of a pitched battle, the victors would be in possession of the field, which was littered with the dead of both sides. Since it was impossible for the defeated to claim back its fallen by force, they would send a herald to ask for a truce to recover them. This request for a truce (named spondai, "libations", after the poured wine that sealed the sacred oath) was effectively an admission of defeat. The winning side already had control over the bodies, and claimed their armour and weapons for its own. The side that had to ask for its dead back was the side that had lost.

This was the accepted way to finish a battle. The request for a truce marked the end of the fighting, and it was nearly always granted. The Spartans did not behave any differently from other Greeks in this respect; after all, they'd want to have their own dead back, too, if they were beaten, and so they followed the Golden Rule. For example, here's what happened after the Spartan victory against the Thebans at Koroneia (394 BC):

The Thebans sent heralds asking to bury their dead under a truce. In this way, accordingly, the truce was made, and Agesilaos went to Delphi and offered to the god a tithe of the amount derived from his plunder.

-- Xenophon, Hellenika 3.4.21

There are only 2 known cases where the winning side refused to give back the dead. In one of these, during the Third Sacred War (356-346 BC), the Lokrians refused to give back some Phokian dead because they regarded the defeated enemy as temple robbers, hated by the gods; they did not deserve the chance to treat their fallen properly. In the other, the Spartan Lysander executed 4,000 Athenian prisoners after the battle of Aigospotamoi in 405 BC, and refused them a proper burial. This was exceptional and probably reflected the character and ambitions of Lysander, as well as the deep hatreds of the Peloponnesian War, more than the customs of his homeland. The Spartans were not known to mistreat the fallen of the enemy any more than other Greeks would mistreat fallen Spartans.

On the other hand, the fact that both sides were keen to recover the bodies of the fallen made the possession of those bodies a form of leverage. The side that controlled the bodies forced the other to admit defeat by asking for a truce. We know that this process was considered humiliating, and that proud armies sometimes insisted on fighting another battle to recover the dead (as some Spartans tried to do after their disastrous defeat at Leuktra in 371 BC). We also know that the recovery of the dead could be considered important enough to relinquish a clear victory in exchange for the last few bodies that had been missed. In short, if you could secure the bodies, you would put your enemy at a moral and strategic disadvantage, and this, of course, prompted shenanigans.

The Thebans were by far the worst offenders, repeatedly using the enemy dead as hostages to secure some further advantage besides victory (such as an oath to retreat from their territory). While the Spartans did not do this, they were always eager to secure undisputed possession of the fallen so as to shame their enemy to the fullest. At the battle of Mantineia (418 BC) they deliberately reformed their battle line in front of all the dead, so that the enemy could forget about reaching any of them without a truce. At Koroneia, they did one better, and dragged all the dead inside of their own lines. None of this was technically against accepted custom, but it did make sure that the enemy would have to go through the process of requesting a truce and admitting that the Spartans had beaten them. In this way, perhaps, the Spartans were unusually calculating or cruel, but their practice was the same as that of the other Greeks.

What did make the Spartans unusual among Greek communities was the treatment of their own fallen warriors. From the Classical period onward, it became standard practice for states like Athens to bring home every citizen who fell in war. They burned the bodies of the dead on the site of the battle, carry the ashes home, and bury them in the Kerameikos in an annual funerary ritual. Other states seem to have had similar rituals, focused on cremating the dead and bringing the ashes back to the city. The Spartans, however, continued the older practice of raising burial mounds in foreign places, near the site of battle, and burying their fallen warriors there. Indeed, a group of Spartan skeletons was found in a tomb right on the Athenian public cemetery; they died nearby, fighting the democratic insurgents of Thrasyboulos in 403 BC. Burial sites in Lakonia itself are rare, and markers with names generally do not have graves beneath them.

Polly Low has argued that this practice was probably about broadcasting to the allies that the Spartans had once, and would again, leave home to fight on behalf of others. It was an important part of Spartan life and the Spartan self-image that Spartans carried war and violence abroad in order to keep their homeland safe. They boasted of fighting and dying elsewhere, while their wives, at the time of the Theban invasion of 370 BC, "had never seen an enemy" (Xen. Hell. 6.5.28). Plutarch preserves a famous anecdote - probably not real, but very illustrative - that an Argive once said to a Spartan, "there are many Spartans buried in our land", to which the Spartan replied, "but there are no Argives buried in ours." By leaving their fallen abroad, the Spartans also showed themselves to be true to their oaths that they would protect their subordinate allies. There could be no more powerful statement of the reliability of Spartan power than Spartan bodies buried far from home.