LLM then Google? "The greening of Mars" is not by Stanley Robinson, but by James Lovelock and Michael Allaby. It doesn't appear to feature moving Mars, but terraforming it using 80's technology. I don't think "Green Mars" by Robinson has Mars being moved either.

There's nothing on Google for Benford and "Martian Transfer", though it's possible he wrote such a story with a different title.