Does a creature with persist come back if it had a -1/-1 counter removed before it died?

Persist reads: 'When this creature dies, if it had no -1/-1 counters on it, return it to the battlefield under its owner's control with a -1/-1 counter on it.' (CR 702.79a). The check is a snapshot of the creature's state at the moment it died (moved to the graveyard), not its history.

So what matters is whether there were any -1/-1 counters on the creature at the time it was last a creature on the battlefield (CR 603.10 — the game looks at the object's last known information before it left the zone). If all -1/-1 counters were removed before it died, it has zero counters when it dies, and persist will trigger.

This is why effects like Solemnity (which prevents counters being placed) or simply removing counters with cards like Fate Transfer or Renounce can 'reset' persist, allowing it to trigger again even on a creature that has already returned once.

Example: Your Murderous Redcap (persist) has already come back with a -1/-1 counter. You use Hapatra's Mark to remove that -1/-1 counter. Then Redcap dies again. Because it had no -1/-1 counters on it at the moment of death, persist triggers and it returns to the battlefield with a new -1/-1 counter.

Citations: CR 702.79a defines persist's condition; CR 603.10 governs using last-known information for triggered abilities that check a permanent's state as it left the battlefield.