It maybe rattling due to the new part of exhaust not being
modded enough.
i think the mainfold maybe rattling against the chassis or something.
I would take it for a long spin making it rattle as much as you can, and then park up, jack up the car, open bonnet and spend a good few minutes looking around engine bay and underneith car.
try and look out for brand new, shiny type marks on the new manifold and the car around the manifold.
If there is some scracthes or dents or even a slight mark - then it could be the exhaust hitting somewhere.
Thats one thing to eliminate.