Healing after being injured by a clay golem is complicated.
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.
First, natural healing:
The damage a clay golem deals doesn’t heal naturally ...
If a character has suffered 10 damage from a clay golem and 30 damage overall, then they can naturally heal 20 of that 30 damage (via resting, etc). The clay golem's curse doesn't stop natural healing for damage not caused by the clay golem.
Next, magical healing:
... 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 statement globally interferes with conjuration spell-based heals. Note that non-conjuration-spell healing, such as a paladin's lay on hands su ability, would not be affected by the curse and would function unimpeded. Once the damage done by the clay golem is healed, then further magical healing is unimpeded. Although no specific mechanism for determining this is provided, it should be safe to assume that the clay golem's damage is healed first whenever possible. In the aforementioned example of 20 points of normal damage and 10 points of clay golem damage, one could assume that a 10-point lay on hands would heal the clay columngolem damage completely, and then further healing could be easily achieved with conjuration healing spells.
Regarding removal via remove curse, I would rule that remove curse would work since the ability is presented similarly to a curse and does not include any language stating that it cannot be removed with removed curse.