  The configuration space $F_2 (M)$ of ordered pairs of distinct points in a
manifold $M$, also known as the deleted square of $M$, is not a homotopy
invariant of $M$: Longoni and Salvatore produced examples of homotopy
equivalent lens spaces $M$ and $N$ of dimension three for which $F_2 (M)$ and
$F_2 (N)$ are not homotopy equivalent. In this paper, we study the natural
question whether two arbitrary $3$-dimensional lens spaces $M$ and $N$ must be
homeomorphic in order for $F_2 (M)$ and $F_2 (N)$ to be homotopy equivalent.
Among our tools are the Cheeger--Simons differential characters of deleted
squares and the Massey products of their universal covers.
