  The analysis of perturbative quantities is a powerful tool to distinguish
between different Dark Energy models and gravity theories degenerated at the
background level. In this work, we generalise the integral solution of the
matter density contrast for General Relativity gravity to a wide class of
Modified Gravity (MG) theories. To calculate this solution is necessary prior
knowledge of the Hubble rate, the density parameter at the present epoch
($\Omega_{m0}$) and the functional form of the effective Newton's constant that
characterises the gravity theory. We estimate in a model-independent way the
Hubble expansion rate by applying a non-parametric reconstruction method to
model-independent cosmic chronometer data and high-$z$ quasar data. In order to
compare our generalised solution of the matter density contrast, using the
non-parametric reconstruction of $H(z)$ from observational data, with purely
theoretical one, we choose a parameterisation of the Screened MG and the
$\Omega_{m0}$ from WMAP-9 collaborations. Finally, we calculate the growth
index for the analysed cases, finding very good agreement between theoretical
values and the obtained ones using the approach presented in this work.
