You're making bold assumptions here. We have no idea how far their empire has spread, for starters. I seriously doubt it's just that one system. And then the military: the heat signals of those ships were massive compared to our biggest ships. If those were military ships, I seriously doubt we could engage even one of them without significant losses.
I have no intention of fighting them now. It seems likely they have a 1500 thermal signature warfare ship, 5x the size of one of ours. Part of that will be the fact we rely on missile weapons, but still. I agree with your post except where you say "as long as possible". If they turn out to be vastly superior, sure, leave them be. If they turn out to be inferior we must take advantage, immediately, because they won't be helping us against future enemies - they'll just be blocking us off from valuable resources.