Is this a law that exists only in America?
I'm in England and I can say that I've never noticed any legal requirement to keep the label on pillows.
Sounds odd to me ... unless it displays safety information
(like: do not swallow, do not set on fire or something equally obvious such as: do not place over somebodys face and press down)
I know that our labels display a CE Mark
(to say that the product is safe/approved safe)
....But if the label was annoying me ... I'd remove it

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Curiouser and curiouser (Cried Alice)