Does counterstrike target?

it's normal damage assigning.

so church of sigma doesn't trigger

and you can't play any actions to counter the dmg

Luckyfer is right, I think we've been playing it wrong.

Here is what the FAQ says:

Counterstrike
Counterstrike is a keyword that allows a defending unit to immediately damage an attacker whenever it is declared as a defender. Counterstrike damage is combat damage that cannot be split among attackers, is uncancellable, and is applied as soon as it is assigned, before any other actions can be taken.

And here is a card with a description:

I don't think it targets.