It should be noted that since most constructs are formed with Thaumaturgy and a lot of power, counter-spelling one is going to be very difficult with a straight up evocation spell. I would highly suggest just burning it to ash, this is supported pretty well by the books. Here are three in spoilers just off hand...Then again, the Warden Swords pretty easily discorporate a zombie, and they're only a 6-shift counterspell.
Harry vs.Harry vs.(click to show/hide)Harry vs.(click to show/hide)(click to show/hide)
I think it would be easy to just make that part of the catch if you want to safe some points when creating the construct, but it doesn't have to be.That makes sense, with Harry occasionally saying fire has this quality when used with this intent.
Mechanically, I think it's a different thing if you attack the construct or the magic that holds it together. In both cases, you burn it with fire, but one would be a regular attack, the other would be a counterspell using fire magic.
I'm not sure if I'm agreeing or disagreeing with Haru.You'd be surprised how often I find myself in that exact same situation.