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I don't know about a C-Clamp but some kind of similar type threaded rod clamp with a knurled turn handle. Body shops often use various types of clamps for spreading or prying open, for pinching or squeezing and to stretch. Maybe the car had some bodywork and it was left clamped onto something by mistake.
I'd take it off. The clamping part is what is sticking down. That looks like the flat bar is wedged in there and a good bump would be what it takes to dislodge. With bad luck, maybe even send it up to a following car.