How damaging would it be? Emerging in teamwork of character skills snapshot?

I don’t know any schools that take that thing seriously. I sat with my son as he took it and I think it’s hard to “do well” unless you are dishonest and answer in a contradictory way every other question.

I wouldn’t worry about it at all. If you are worried call your AO and talk to them about it. The more feedback they get that the test is absurd the less they will place value in it.