So we clearly are expanding some kind of prohibition into quadrant III.What could it be? It is not going the be "how do they serve?" because that is what we are about to use to tell us not to expand the the prohibition there.
That is to say we might think such and such a thing so we have a verse to exclude it. But I am wondering on the Gemara itself why would we think to expand it? Well the Gemara itself gives a reason. What is it with exposing oneself to Peor is liable, so also all types of service that are not honorable are liable. But how does that reasoning help to expand bowing to serve that is dishonorable that is its way that Tosphot requires in order to answer his question?
Actually I dont think this last answer is right, and rather the real reason we would have expanded the prohibition into quadrant III is just because idolatry is forbidden. i.e from the verse "least he will go and serve"