Physically the only relevant (measurable) quantity is F.

Since F=2dA, adding d to A gives:

A' = A + d

F' = 2dA' = 2dA + 2d(d)

... but d(d(anything)) is zero (by the definition of the 'd' operator - see p. 232) so:

F' = 2dA = F

...i.e. adding d leaves F unchanged!