In Sandifer v. United States Steel Corp. (12-417), Eric Schnapper listed several forms of courtroom attire. He even mentioned the neck brace! But he omitted the neck doily.
In ordinary parlance, not everything an individual wears would be referred to as clothes. There are examples of that in this courtroom: Glasses, necklaces, earrings, wristwatches. There may be a toupee for all we know. Those things are not commonly referred to as clothes.
Personally, I think of it more as a garnish.
And for lol, Justice Scalia took umbrage that someone in the Court wore a toupee!
JUSTICE SCALIA: I resent that.
Totally serious question for anyone who knows. Is the neck doily put on in the robing room? Does RBG keep a slew of them there? Or are they kept in chambers? Does she ever dither on which one to pick? How long does a neck doily take to put on? If anyone knows the answer, you know where to reach me.