  The $G_\delta$-modification $X_\delta$ of a topological space $X$ is the
space on the same underlying set generated by, i.e. having as a basis, the
collection of all $G_\delta$ subsets of $X$. Bella and Spadaro recently
investigated the connection between the values of various cardinal functions
taken on $X$ and $X_\delta$, respectively. In their paper, as Question 2, they
raised the following problem: Is $t(X_\delta) \le 2^{t(X)}$ true for every
(compact) $T_2$ space $X$? Note that this is actually two questions.
  In this note we answer both questions: In the compact case affirmatively and
in the non-compact case negatively. In fact, in the latter case we even show
that it is consistent with ZFC that no upper bound exists for the tightness of
the $G_\delta$-modifications of countably tight, even Frechet spaces.
