protective slip or cover for the top of the back bumper

Circled in this image, is there a protective slip or cover for the top of the back bumper? When my dog jumps in the back she is scratching the bumper with her paws

Depends on where you live! BMW DOES have one they sell in many markets, but BMWUSA chose not to import it. My sister and brother-in-law are in England, and they sent me one...works fine. Took all of a few minutes to install...clean the surface with the supplied cleaning pad, then, stick it on! You can find it on the www.bmw.co.uk website, or most others around the world. It's available in a few colors from the manufacturer, but BMW only sells it in black (if I remember correctly). If you were in England where they're made, you can get them in more colors.

Your image isn't showing, but I can imagine that you want to protect the flat top surface of your rear bumper. Several i3 drivers like this generic bumper guard. I might order this custom-fit clear bumper guard. Unfortunately, neither wraps around the back edge which could still get scratched.

The BMW one wraps the edge by maybe 1/8-1/4" or so and perfectly follows the curve. It's a matt finish so it doesn't show scratches it otherwise might. I carry a folding recumbent tricycle in the back, and it has saved the bumper cover from nicks and scratches. For a 'simple' piece of plastic, it's expensive, but so is repainting the car, too. I can't find it on their website anymore and really do not remember the maker! But, the company is in England, and it has (had) a BMW part number on it. They picked it up at the BMW dealership there for me. It was actually cheaper to buy it at the BMW dealership than from the maker...