Not necessary, because even if cornmeal is used to clean out farm-raised mussels, the author is only arguing that he doesn’t need to use cornmeal. It may be that many people still use cornmeal when they don’t need to; that doesn’t undermine the argument.

Not necessary, because other contaminants can be cleaned out by other steps. The author merely believes that he can skip the cornmeal step. But there may be other steps necessary to get rid of other contaminants.

Not necessary, because we have no reason to think taste plays any role in the author’s reasoning. Let’s say cornmeal does affect taste — thta doesn’t suggest a reason the author can’t skip the cornmeal step.

Not necessary, because even if the recipe was written after farm-raised mussels became available, the recipe might have been assuming people didn’t have ready access to farm-raised mussels. In any case, the author’s argument is that he can skip a step in the recipe, so it’s not clear why he’d have to assume anything about when the recipe was written.

Necessary, because if it were not true — if the mussels the author is using are NOT from a seafood market — then the author can’t assume that the mussels do not contain sand. In other words, if (E) were not true, the author might not be able to skip the cornmeal step.