The door handles on my Brava are also the same (all four in fact). I think it is just the 'soft rubber' materials used on the outside of the handles, which are not really suited to our environment, thus erode over time due to wear & tear, weather, and the like. I much prefer hard plastic. I had thought about getting them changed, but did not see the point if the replaced ones will erode later on. It's not too ugly...so probably live with it.
Another member "Trev_M" described something in the Technical section about fixing the heat shield. You might want to look over there, and see if it helps you out. I had the similar problem quite some time ago on a different make of car and I did a similar thing as Trev_M suggested to sorted it out.
I wouldn't remove the heat shield because I think it helps to keep the heat from your hot exhaust pipe from eating into (or melting) the bottom of the car over time (perhaps not MOT related initially, but will certainly become a MOT issue if you have to do welding down there). The heat shield is a meshed thing to help distribute the heat. I also think it helps to keep some of the splashed water out off the underside of the car, thus may help to slow down rusting process down there (a little perhaps !).
