dnd 5e – Would a teleporter also teleport a wizard's hand?

Suppose I have a trap that, when touched, teleports the creature that touched it to a new area. The players suspected the trap, and a magician tried to activate it with the wizard's hand.

I interpreted the result as the trap that teleported into his wizard's hand. The players protested and we did not get a clear answer about what should happen to the wizard's hand.

Would the result change if the players could see where the trap teleported?