  We study the problem of recovering a function of the form $f(x) = \sum _{k\in
\mathbb{Z} } c_k e^{-(x-k)^2}$ from its phaseless samples $|f(\lambda )|$ on
some arbitrary countable set $\Lambda \subseteq \mathbb{R} $. For real-valued
functions this is possible up to a sign for every separated set with Beurling
density $D^-(\Lambda ) >2$. This result is sharp. For complex-valued functions
we find all possible solutions with the same phaseless samples.
