#marked damage

It won’t die if it previously took damage from a source with deathtouch in the turn, though, as the check for deathtouch damage only applies to the next time state-based actions are checked after the damage is dealt.

Remember, normal damage doesn’t reduce a creature’s toughness, no matter what Magic Arena would have you believe. The damage just stays marked on the creature until the turn ends and waits to see if the damage ever equals or exceeds the creature’s toughness.

An indestructible creature can never be destroyed by marked lethal damage. In the situation you describe, you’ll have an indestructible 3/3 creature with 3 damage marked on it. Its toughness would need to be reduced to 0 or less for a toughness-reducing effect to kill it. (Normal damage doesn’t reduce toughness.)

Normal damage doesn’t reduce a creature’s toughness, no matter what Magic Duels would have you believe.

Damage stays marked on a permanent until the cleanup step, even if it stops being a creature.