  Region of trapped null geodesics hidden inside of extremely compact objects
is of astrophysical importance because of trapping of gravitational waves, or
neutrinos. The trapping effect of null geodesics was extensively studied for
spherically symmetric extremely compact objects. Recently, influence of
rotation of the extremely compact objects on the trapping of null geodesics was
treated in the simplest possible model of internal linearised
\mbox{Hartle--Thorne} spacetime with uniform energy density distribution and
uniform emissivity distribution of null geodesics. Here we extend the study of
the rotation influence on the trapping effect in the case of linearized
\mbox{Hartle--Thorne} spacetimes based on the Tolman VII spherically symmetric
solutions, where we assume the emissivity of the null geodesics proportional to
the energy density of the Tolman VII object having quadratic radial profile. We
demonstrate enhancement (suppression) of the trapping effect in the case of
counter-rotating (co-rotating) null geodesics due to the behavior of the
effective potentials and escape cones of the null geodesics in the linearised
Hartle--Thorne--Tolman VII spacetimes. In dependence on the parameters of these
spacetimes we determine the "local" and "global" coefficients of efficiency of
the trapping and compare the results to those related to the rotating
spacetimes based on the internal Schwarzschild spacetimes. We demonstrate that
in the Tolman VII spacetimes the trapping is more efficient, being allowed in
objects with radii larger than those of the trapping internal Schwarzschild
spacetimes, occurring even for $R>3.3M$.
