I guess this could be a bug that came up in one of the recent updates as I don't remember C4DtoA behaving this way in the past. When using a Background object with white material in combination with an HDR image as light source on a Skydome, the HDR image shows through a transparent object.
My current workaround is to put a white plane behind the scene to "block out" the HDR image. Is there a better solution or is this a bug?
A ray first hits the skydome and than the background, but the background is disabled for transmission rays by default, that's why the HDR shows up.
Go to the Arnold Render Settings > Diagnostics > User options and type background_visibility 9 in the field. It should make the background visible for camera and transmission rays.
The Background object actually overwrites background_visibility, that's why it's not working, sorry. If it's just a color, as a workaround you can use a ray_switch_rgba shader in the skydome material and use the color as the specular transmission. However it does not work when you want to use a texture as the background. I don't think we have a workaround for that at the moment. But hopefully we can add support for transmission soon.