I would say that disputing is softer than denying in general. I may dispute something's accuracy without denying it outright. I might dispute that something necessarily means what someone claims without completely denying that it could mean that.
That said, the difference between C and E is not in the disputing/denying element. Rather, it lies on what the answer choices say is being disputed or denied. C is describing a stated premise while E is describing an unstated premise
