  The chromo-polarizability of a quarkonium state is a measure of the amplitude
of the $E1$-$E1$ chromo-electric interaction of the quarkonium with soft gluon
fields and can be measured in the heavy quarkonium decays. Based on the chiral
unitary approach, formulas with modification caused by the $S$ wave $\pi\pi$
final state interaction (FSI) for measuring the chromo-polarizabilities are
given. It is shown that the effect of the $S$ wave $\pi\pi$ FSI is very
important in extracting chromo-polarizabilities from the experimental data. The
resultant values with the FSI are reduced to about 1/3 of those determined
without the FSI. The consequences of the FSI correction in the $J/\psi$-nucleon
scattering near the threshold are also discussed. The estimated lower bound of
the total cross section is reduced from about 17 mb to 2.9 mb, which agrees
with the experimental data point and is compatible with the previously
estimated values in the literature. In order to understand the interaction of
heavy quarkonia with light hadrons at low energies better and to obtain the
chromo-polarizabilities of quarkonia accurately, more data should be
accumulated. This can be done in the $J/\psi \to \pi^+\pi^-l^+l^-$ decay at
BES-III and CLEO-c and in the $\Upsilon \to \pi^+\pi^-l^+l^-$ decay at B
factories.
