It is of note that Gertrude uses the plural of brow here.
Usually – the brow is the forehead and the most likely part of the body to dab with a handkerchief if one is sweating.
But she says “brows” plural. And the word brows, when it is this plural, usually suggests the eyebrows – as in “that model has her brows done at the local salon.”
Is Gertrude telling Hamlet to rub his eyebrows? Or is she speaking to both fighters suddenly – wishing for Laertes to rub his brow as well?
I doubt that.
It is most likely that she means brow.
And according to my friend ETYMOLOGY online – we get the word brow for forhead from the eyebrows – that brow meant eyebrow first and expanded to cover the entire forehead in around 1200.
So maybe Gertrude is just a 1200 girl with her “brows.” Also – I’ve just realized as I wrote these words how weird English is – because browse sounds exactly like brows and means something entirely different.