Quote - Are you using a sky backdrop or are they glass panels behind the car?   It seems odd if it's adding shadow to glass that it would effect the sky.

There are semi transparent glass panels behind the car. Of course in daylight you can't see anything behind it so it looks more or less like a simple mirror, so what you see is the reflection of the sky behind(!) the camera. The roof is from the same material as the columns. It should protect against rain and wind, but shouldn't block much light.
It makes sense if you'd look at a scene where it was included, but as it is now the viewer wonders where this shadow comes from, so I'll exclude it in the next render.

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If you have any object that you don't want to receive shadows (including a plane if you're using a photograph for the sky) open the material to edit it and UNCHECK 'Receive shadows' - that'll fix it

Hey, that's cool. I already knew that I can configure light to not CREATE any shadows, but it's new to me that I can have objects which do no RECEIVE any shadows.
Learning something new each day. Thanks a lot