The support establishes that most voters will perceive Grenier as insincere. This triggers (A), which confirms that Grenier therefore probably won’t win them over—meaning she'll probably lose. By logically connecting the pundit's premise and conclusion, (A) bridges the gap and justifies the argument.

This would hurt the argument, not help justify it: the pundit's argument requires voters to notice Grenier's changing stance on an issue, or else it couldn't affect her chances of winning. (B) doesn't lead to the conclusion that Grenier will likely lose.

Like (B), this undermines the pundit's argument, which relies on voters caring about Grenier's changing views—that's the whole reason the pundit predicts Grenier will lose! We don't know whether voters agree with Grenier's current views, so this principle isn't triggered, and therefore can't bridge to the conclusion.

We have no idea how voters feel about Grenier’s understanding of their financial concerns, so (C) is just not relevant to the argument. It doesn't apply to the facts that we're given, so it can't help lead us from there to the conclusion.

The pundit states as a premise that voters will see Grenier as insincere, so we don't need more confirmation of that. What we need is a bridge from that perception of insincerity to Grenier's electoral chances. Because (E) doesn't take that next step, it's not helpful.