Does damage marked on a creature get removed at end of turn even if the creature gained indestructible after being damaged?

Damage marked on a creature is removed during the cleanup step at the end of every turn. This happens automatically under CR 514.2, which states that all damage marked on permanents is removed at the start of the cleanup step. This process is completely independent of any abilities the creature has, including indestructible.

Indestructible (CR 702.12) only prevents a permanent from being destroyed — meaning it stops the game from moving a permanent to the graveyard due to lethal damage or a 'destroy' effect. It does NOT prevent damage from being marked on the creature, and it does NOT affect the cleanup step's removal of that damage.

So the sequence matters: if a creature has lethal damage marked on it, state-based actions (CR 704.5g) would normally destroy it. Indestructible stops that destruction. But once the cleanup step arrives, the damage is wiped away regardless — the creature simply survives to the next turn clean of any damage counters.

Example: Your opponent's 2/2 creature blocks your 5/5 and takes 5 damage. In response to a later spell, your opponent gives it indestructible until end of turn. State-based actions see the creature has lethal damage but cannot destroy it thanks to indestructible. Then, during the cleanup step, all 5 damage is removed from the creature, and it survives the turn as a fresh 2/2 (assuming indestructible has worn off, but that doesn't matter for the damage removal).

In short: indestructible saves the creature from being destroyed by lethal damage during the turn, and then the cleanup step erases the damage as normal. The two effects operate on entirely different parts of the rules.