The Clay Golem’s Extraordinary Ability Cursed Wound reads:
The damage a clay golem deals doesn’t heal naturally and resists healing spells. A character attempting to cast a conjuration (healing) spell on a creature damaged by a clay golem must succeed on a DC 26 caster level check, or the spell has no effect on the injured character.
This effect only relates to the damage directly dealt by a Clay Golem and not to any other additional damage a creature takes or has taken before or thereafter from other sources. The "curse" affects only the wounds and not the creature as a whole. So it's important to track the damage dealt by a Clay Golem seperately.
If the damage is healed, the creature won’t suffer any further impairments.
It’s hard to say whether a Remove Curse spell would work here. Normally, curses are caused by magic or supernatural abilities rather than extraordinary abilities. On the other hand, a "curse" is something -at least to my knowledge- which it is not clearly defined anywhere in the rules.
As a DM, I would allow to use Remove Curse to get rid of the "not healing“-property of the damage taken – but not of the damage itself.