As Teflon has mentioned Bob, the rust starts from behind the door uprights, where the inner sections are spot welded on. Unfortunately, the black paint can't get into the joint, but moisture does, and hey presto....corrosion
Use a thin rust proofing fluid like Dinatrol & allow it to seep into the joints on the new finishers before letting A&M fit them
Marinabrian is completely correct, you only need to get the finishers removed to paint it properly. Removing & refitting the screens brings the risk that they might just leak after refitting. So if the car is currently dry & leak free, I'd ask them to only remove the trims but leave the screens in place. I'm sure they will understand this.
Lastly, I can vouch for the quality of their finished jobs Brian, I collected a Stag from them a couple of months back and the paintwork was like glass, mirror finish and a truly stunning depth to the shine. I couldn't fault it. You get what you pay for...