I find myself somewhat baffled by this analogy. I mean, I get it on the SAT level in that make-up is to a harlot’s cheek as Claudius’ painted word is to his deed. I get that they are both covering up ugliness, with surface beauty.
What’s baffling me is the “to the thing.” That is, is it that the make-up is personified and finds the face it is covering unattractive? Or is it “to” as in “compared to” that is, if we compare these things, the make-up is worlds away from the harlot’s cheek. Or – even more likely – the make-up (and skill of making up) are just as ugly as what it is covering up, that in covering ugliness, the plastering art becomes ugly, too, even though it seems beautiful.
I am also intrigued that two references to make-up happen in the same scene from two different characters. Is Hamlet somehow hearing this aside? And it inspires him to say something about make-up a little bit? Probably not – asides are generally not heard by other characters . . .but it’s an interesting possibility. It might undercut the tension of the Mousetrap somewhat, though.