  In this work we deal with the preservation by $G_\delta$-refinements. We
prove that for $\mathrm{SP}$-scattered spaces the metacompactness,
paralindel\"ofness, metalindel\"ofness and linear lindel\"ofness are preserved
by $G_\delta$-refinements. In this context we also consider some other
generalizations of discrete spaces like $\omega$-scattered and $N$-scattered.
In the final part of this paper we look at a question of Juh\'asz, Soukup,
Szentmikl\'ossy and Weiss concerning the tighness of the $G_\delta$-refinement
of a $\sigma$-product.
