If you put out are fire, where does the smoke go instead?

The methane was produced by a bacteria, it is never produced to go anywhere if you get rid of the bacteria. The trade off might be poorer digestive efficiency if the cow relies on this bacteria to break down some common molecule. Although it could just as easily be the case that the bacteria was introducing inefficiencies.

> The trade off might be poorer digestive efficiency if the cow relies on this bacteria to break down some common molecule.

We drifted a little, but the top-level comment of this same thread started out to suggest that if any, the effect might even be positive for the cow.

From the article: "When added to cow feed at less than 2% of the dry matter, this particular seaweed completely knocks out methane production. It contains chemicals that reduce the microbes in the cows’ stomachs that cause them to burp when they eat grass."

It is simply not produced. Methane is CH4. The carbon goes into CO2 instead (which is bad, but not as bad for the environment as methane).