If a Mage Hand triggers a trap (in my case, by screwing a lightbulb into a booby-trapped socket) or otherwise takes damage from some effect, what happens to it? Does it just sit there and ignore the damage? Does it go "poof"? Does the caster have to make a Concentration check to keep the spell going? Does the caster take the damage in lieu of the Mage Hand? Does either the Mage Hand or the character have to roll a saving throw?
Mage hand doesn't make a hand, therefore there is nothing to effect. Reread the spell description. It's just telekinesis on one object. If your game plays that there's a "special effect" of a hand that appears, that's fine, but has no bearing on the spell effect, which has no such thing.