V10lentray is correct that such a situation would be a rather unusual decision, but the question is still valid as to what happens if you were to choose to use the Teleport Trap first.
It is important to recognize that Mangler Caltrops is neither a melee attack nor a ranged attack. It is similar to a damage barrier in that range does not matter for it. Therefore, after you teleport you are still a valid target for the Caltrops and you did trigger them, so they would still get their attack. You could again think of them as similar to a damage barrier and justify these mechanics as though the attack happened concurrent with entering the zone, and you're just now getting to the part of actually applying the effects.
An argument could be made that the rules on page 7 of the FAQ regarding changing the range or target of a spell or attack would apply in this situation, but technically the change in range occurred before the attack began, even though the trigger event already occurred, and so I do not believe that would apply. It doesn't specify it in so many words, but I think an attack has to actually begin, ie go past the Declare Attack Step, before a change in range or target could possibly cancel it.
