Makilla
1437
I don’t think they will polish out the scratches on the bridges.
Usually bridges are made of brass and rhodium plated to have the white color. So basically if they remove the scratches the plating will also be removed. They will surely replace the scratched parts with new ones.
The person who worked on your watch is definitely a car technician and not a skilled watchmaker. Scratching the movement like this requires very bad handling. On top of that if you send it to Patek they will charge an arm and a leg for parts replacement including the solid gold rotor.
Best of luck and do let us know what you end up doing!
Laurent