  We consider gravitational quasinormal modes of the static and
spherically-symmetric dirty black holes in the effective theory of gravity
which is renormalizable at the two-loop level. It is demonstrated that using
the WKB-Pad\'e summation proposed in \cite{jaOp} one can achieve sufficient
accuracy to calculate corrections to the complex frequencies of the quasinormal
modes caused by the Goroff-Sagnotti curvature terms. It is shown that the
Goroff-Sagnotti correction (with our choice of the sign of the coupling
constant) increases damping of the fundamental modes (except for the lowest
fundamental mode) and decreases their frequencies. We argue that the methods
adopted in this paper can be used in the analysis of the influence of the
higher-order curvature terms upon the quasinormal modes and in a number of
related problems that require high accuracy.
