If a unit controls a battlefield and cannot take damage, do the attacking units go back or take the battlefield?

The attacker gets recalled back to base. The defending unit that cannot take damage survives combat, so defenders remain at the battlefield — and per Rule 461.1.a.2, attackers are recalled whenever defenders are still present.

Here's the sequence:

1. Combat Damage — The attacker deals damage normally, but the defender's "can't take damage" effect prevents it from being marked. The defender's own damage (if able) hits the attacker. Per Rule 460.2.c.9, a unit that can't take damage is exempt from lethal assignment considerations, but damage is still assigned and dealt to it — it just has no effect.

2. Resolution Step (Rule 461) — Combat Cleanup heals all units, then recalls attackers if any defenders are still present. Since the immune defender is still standing, the attacker is sent back to base. The defender then wins the combat and re-establishes control (clearing Contested status).

The defending player keeps the battlefield — no conquer happens since they already controlled it. The attacker goes back empty-handed.