I think this might help. In a previous post this week, bagginsbill explained why this happens. Without paraphrasing is detailed and wonderful explanation, the short answer is to choose the option "render over black". Briefly, it has to do with the edges of the rendered object blending with the character to produce a color that it not truly invisible and not truly the color of the object and that's what the edge is.

If I didn't explain this correctly, I apologize. But I tried it and it worked.