  We obtain well behaved interior solutions describing hydrostatic equilibrium
of anisotropic relativistic stars in scale-dependent gravity, where Newton's
constant is allowed to vary with the radial coordinate throughout the star.
Assuming i) a linear equation-of-state in the MIT bag model for quark matter,
and ii) a certain profile for the energy density, we integrate numerically the
generalized structure equations, and we compute the basic properties of the
strange quark stars, such as mass, radius and compactness. Finally, we
demonstrate that stability criteria as well as the energy conditions are
fulfilled. Our results show that a decreasing Newton's constant throughout the
objects leads to slightly more massive and more compact stars.
