I'm not sure what the rules were in 1.0 because I never had a chance to use debris. However I read an article that said the stress was received after the Check pilot stress step. However I see no such wording in the new rules.

I'd like to know if I can do a green manoeuvre through the debris field and clear the stress that it gives me.

You cannot. The stress from Debris Clouds arrives after the 'Check Manoeuvre Difficulty' step.

Ah Ha, is see. Because the removing stress is part of the complete 'execute manoeuvre' stage.

Thanks