12 Mini Countryman AWD. A metal on metal like grating noise developed in Right Front wheel only while in reverse, not braking and never forward. What could it be?
According to a different motor vehicle type forum, your options for trouble are varied.
One suggestion is that the pads are worn unevenly, which causes unusual vibration when the movement "re-aligns" the pads. This seems to be on the low end of probability.
Another low end suggestion is that the wear indicators are contacting the disk, due to the change in angle when braking in reverse.
More helpful is the suggestion of rust on the disks, something that would require to have some time passing between parking and movement, sufficient to allow rust to form. On some vehicles (mine!) that can be as short as two days. I get forward grating sound for a stop or two after the vehicle sits.
Now to the nitty-gritty. One forum posting party discovered that he had not properly torqued his caliper bolts after performing service. If you've not performed any work on your front wheels, you may be able to disregard this suggestion.
More of a concern is the fellow who posted that he's discovered cracked rotors. Because disk brakes are so easily exposed, this should be something you can check by jacking up the vehicle and removing the wheel.
In the days of drum brakes, it was important to evenly torque the lug nuts in a star pattern to reduce/prevent distortion of the drum. It's not so much of a concern with today's disk brakes, but it's still a good habit to re-tighten the nuts in a cross-over pattern, a bit at a time until all are secure.
While you have the wheel off for visual inspection, you should move it in reverse to avoid overlooking the obvious. I can't tell you what would be obvious, as it's only obvious if you see it clearly when you look at the wheel. Something stupidly obvious would be a metal tag that floats in forward and snags in reverse, but that's pretty unlikely. Why would there be a tag near the brake assembly?
Look for something that shifts position when moving the wheel from forward direction to aft. Your post suggest that it doesn't happen when braking, which makes it more likely you should be able to see while manually rotating the wheel.