My Car Makes Grinding Noises When I’m Backing Up

I have a 2001 Mitsubishi Eclipse with 105,000 miles on it. For the past year or so, it has occasionally made these odd grinding sounds from the rear when I start the car and put it in reverse, and continues to make the grinding noise until I’ve stopped moving backward and put the car in “drive”. The car jerks a bit when it does this, as if it’s idling too low and is trying to die, but it *never* does this when I’m in drive, or when I’m in reverse but have have been in the car for a while: it’s only when I first start the car and am backing up.

I’m certain that it’s not the brakes, because then it seems that the grinding noise would come from the front (it’s a front wheel drive car) rather than the rear, and eroded brake pads wouldn’t make the car shudder.
I’m concerned that it might be some crazy transmission problem. Any ideas??

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