January 2017
I've already destroyed 4 Zombie Teleporter in Ops, and the Quest did not trigger.
April 2017
I think this is only meant to be for matches of turf takeover, and not ops. I would try that, and see if it works for you.
April 2017
I've been playing GW2 for a long time and I don't believe that the Quest has ever recognized the destruction of an Ops-based teleporter as legitimately fulfilling the requirement; it's pretty much intended for Turf Takeover teleporter destruction because Ops pretty much just hands you that victory with little resistance.
April 2017 - last edited April 2017
It only works in multiplayer, but you can do it solo. Start an empty solo game (on crazy to maximize xp for the building and destroying), build the relevant teleporter on the first stage, then switch teams and destroy it. Sometimes you can combine this with a multiplayer quest for something like capturing bases by continuing with the game until you've met the other quest requirements.
This one ticks me off. If it's a star quest, then make it work in ops. Otherwise, make it a multiplayer quest. I don't buy the "too easy in ops" reasoning - many of these star quests are ridiculously easy to complete.