An earlier post mentioned Klaus Lackner, physicist at Columbia University, who proposes artificial trees to suck carbon out of the air. The trees suck in carbon dioxide for storage under the ocean-floor in disused oil or gas fields.
Another contender for this award and working along similar lines is Wow Energy, a Texan company that builds equipment to clean the air from pollutants. They originally developed their technology to provide a cleaner process at the point
of emission, e.g. when burning fossil fuel at a power plant ("clean coal"). Note that the Branson award is to clean ambient air from greenhouse gas emissions, as opposed to scrubbing done at power plants or through filters in cars, but if it works well for ambient air then that would be great. For more details, go to Wow Energies