  We investigate the contributions of the Friedmann-Lema\^itre-Robertson-Walker
metric of the standard cosmology as an asymptotic boundary condition on the
first-order approximation of the gravitational field in Moffat's theory of
modified gravity (MOG). We also consider contributions due to the fact that the
MOG theory does not satisfy the shell theorem or Birkhoff's theorem, resulting
in what is known as the "external field effect" (EFE). We show that while both
these effects add small contributions to the radial acceleration law, the
result is orders of magnitude smaller than the radial acceleration in spiral
galaxies.
