  In addressing the B --> eta' K puzzle, there has been a considerable hope in
the literature to resolve it by the QCD anomaly contribution to the b --> s
eta' amplitude. This contribution corresponds to the electroweak b --> s g* g*
transition followed by the off-shell gluon fusion g* g* --> eta'. In the
present paper we perform a critical reassessment of this issue. We show that
for the hard virtual gluons in a loop there is a well defined short distance
amplitude corresponding to a remnant of the QCD anomaly. However, we find that
it cannot account for the measured amplitude.
  In addition, we point out that the reduction of the gluon fusion vertex for
the off-shell gluons is compensated by an absence of the claimed suppression in
the electroweak vertex, and that some nonperturbative contributions related to
the QCD anomaly may still be viable in explaining the physical B --> eta' K
amplitude.
