  Efficient computation of the quadrupole light deflection for quasars/quasars
and solar system objects within the framework of the baseline Gaia relativity
model (GREM) is discussed. Two refinements have been achieved with the goal to
improve the performance of the model: First, the quadrupole deflection formulas
for both cases are simplified as much as possible considering the Gaia nominal
orbit (only approximate minimal distances between Gaia and the giant planets
were used here), physical parameters of the giant planets and the envisaged
accuracy of 1 microarcsecond for individual systematic effects. The recommended
formulas are given by Eq.(40) for stars/quasars and by Eq.(81) for solar system
objects. Second, simple expressions for the upper estimate of the quadrupole
light deflection have been found allowing, with a few additional arithmetical
operations, to judge a priori if the quadrupole light deflection should be
computed or not for a given source and for a given requested accuracy. The
recommended criteria are given by Eq.(45) for stars/quasars and by Eq.(92) for
solar system objects. Additionally, the quadrupole Shapiro effect for solar
system objects is reconsidered. A strict upper bound of quadrupole Shapiro
effect for solar system objects is given in Eq.(109).
