Re: I appeal to your better judgement
Google can appeal against the fine, or to the court's better sense, or for a fair trial.
Indeed they can.
They can also just appeal -- with all information about the appeal left unsaid ("Bails fall and Google appeals").
And they can also appeal the fine, without describing whether they are appealing against the fine, or to the court's better sense, or for a fair trial or something else -- just that it is regarding the fine.
All perfectly acceptable to this, and to most, English speakers. Just because you wouldn't say it does not make it ungrammatical.