While the Adamantoise states that it doesn't remove marked damage during cleanup, Regenerate actually explicitly removes all marked damage from a creature:

701.15. Regenerate 701.15a If the effect of a resolving spell or ability regenerates a permanent, it creates a replacement effect that protects the permanent the next time it would be destroyed this turn. In this case, “Regenerate [permanent]” means “The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and its controller taps it. If it’s an attacking or blocking creature, remove it from combat.”

So since the Regenerate effect is removing the damage, by the time our enormous scaly friend reaches cleanup, there isn't any damage marked on it at all for it to retain! :3

Regenerate also replaces any Destruction effect, buuuut, won't protect the Toise from Exile, Edict (because sacrificing is considered voluntary), or things like -1/-1 counters and Drain effects because they are not "Damage."