If a permanent enters the battlefield with counters and is immediately bounced, do the counters matter?

When a permanent enters the battlefield with counters (via replacement effects, abilities like 'enters with N +1/+1 counters,' etc.), those counters exist on the permanent while it is on the battlefield. Counters are not an intrinsic property of the card itself — they are a game object attached to the permanent (CR 122.1).

If that permanent is then 'bounced' (returned to its owner's hand), it changes zones from the battlefield to the hand. When it leaves the battlefield, it becomes a new object with no memory of its previous existence on the battlefield (CR 400.7). All counters that were on it simply cease to exist — they do not follow the card to its new zone.

This means the card in hand has no counters on it. If it is cast and enters the battlefield again, it starts fresh. Any counters would need to be re-applied through replacement effects or other abilities at that time.

Concrete example: You cast Managorger Hydra, which enters with no counters (it gains +1/+1 counters as spells are cast). Suppose it has accumulated three +1/+1 counters. Your opponent bounces it with Unsummon. The Hydra returns to your hand as a plain card — the three counters are gone. When you recast it, it enters with zero counters again.

The only narrow exception is if a card specifically tracks something across zones or has an ability that functions in other zones, but standard counters on permanents do not do this (CR 400.7, 122.2).