From the article (just a proposal so far):
"Methane is challenging to capture from air because its concentration is so low. However, the authors point out that zeolite, a crystalline material that consists primarily of aluminum, silicon and oxygen, could act essentially as a sponge to soak up methane. “The porous molecular structure, relatively large surface area and ability to host copper and iron in zeolites make them promising catalysts for capturing methane and other gases,” said Ed Solomon, the Monroe E. Spaght Professor of Chemistry in the School of Humanities and Sciences.
The whole process might take the form of a giant contraption with electric fans forcing air through tumbling chambers or reactors full of powdered or pelletized zeolites and other catalysts. The trapped methane could then be heated to form and release carbon dioxide, the authors suggest."
"A zeolite array about the size of a football field could generate millions of dollars a year in income while removing harmful methane from the air."
One major point is that these scientists are saying that methane is much more harmful than CO2... enough so that it can actually make sense to try to convert it to CO2 so it would be less damaging.