Yes mate that is the door protector strip, it does come off because a lot of people have smooth bravos, but it does leave holes and makes, so after removeing it will need smoothing over and filling then spraying.
They are very easy to remove. they're held on by a plastic clip at each end and then just adhesive strips along the length. Just carefully insert soemthing down the back at each end to pop the clips out and then pull away the adhesive. However, the adhesive will need replacing as the clips are not enough to hold it flush with the car.
The only things to be wary of are
1) Take great care when removing them not to snap of the clips.
2) The long ones on the door are a pain in the ar*e as the stuff they're made out of is very maleable but once bent tends to stay that way so its hard to remove them and keep them straight and flat. I learnt this when removing one at a scrappys and ending up with it curled completely round me !
The other thing to do would be to buy new ones from Fiat, they're about £15 per trim I think.
I took the strip off from one side of my Bravo and I vowed never to even look at them again.
That's cus once you bend them, you can never (I mean never) get them back into their original shape. And how can you take them off without bending them? I ended up spending £50 for new trims at Fiat.