I view the paladin as being a party to the contract where the orc's surrender is accepted and release given subsequent to cooperation. If the paladin did not intend to accept the orc's surrender and cooperation, he should have spoken up earlier. To do otherwise is dishonest. It's like ordering a meal in a restaurant, eating it, and then leaving without paying because "I thought the prices were too high, and anyway I never said I was going to pay."
He also made his party member a liar by voiding the promise of safe conduct; that dishonors the party member and destroys the unity of purpose of the party. The paladin's action also diminished the dignity of the orc. Either you treat the orc as not possessing any dignity as a sentient being- in which case you don't treat or negotiate with him at all- or you give him at least the dignity to defend himself. The paladin dishonored himself by his behavior.
I might have an NPC cleric of the paladin's faith scold him (making the points I made above) but I wouldn't strip him of his powers; I try not to be that kind of DM. I would try to arrange the consequences more subtly- like having the paladin rely on the honesty and discretion of a Lawful Good institution, and have his trust be violated. Without any sign of divine disapproval of the institution. I would also try to have (lawful) evil opponents treat him honorably (respecting deals, etc.) - enough so that he recognizes the benefit of this kind of behavior.
But subtly, subtly. It should improve the ability of the player to engage in moral reasoning. Not be some kind of ham-fisted exercise of the DM's arbitrary authority.