That is a reflection of somewhat more stable air being channeled through the Chevala pass from the Bay of Campeche into the Gulf of Tehuantepec around the west side of Beta, definitely. It's a fairly common occurence with a tropical cyclone in the Gulf or western Caribbean and can sometimes help spin up a tropical system in the Pacific when there is an active wave along the ITCZ...i.e. it can give that extra little oomph/kick to a wave to help it develop if it was on the borderline beforehand.

But for now, though, you aren't going to see such a thing -- air in the Gulf is pretty dry & relatively cool and you're getting some stratocumulus development as a result of the temperature differential between the sea surface and near-surface air. Cool to watch, though.