Can combing bent evaporator coil fins damage it?
You could follow the manufacturer's advice - they tend to know what they are talking about...

But if you insist on trying to straighten those bent fins, then use something that will not poke a hole in any of the tubes and go gently.

I have done this for similar heat exchangers with that type of fin and it is possible. Also for heat exchangers which have loops of wire, go slowly and carefully.