  Recently, we introduced the twist polynomials of delta-matroids and gave a
characterization of even normal binary delta-matroids whose twist polynomials
have only one term and posed a problem: what would happen for odd binary
delta-matroids? In this paper, we show that a normal binary delta-matroid whose
twist polynomials have only one term if and only if each connected component of
the intersection graph of the delta-matroid is either a complete graph of odd
order or a single vertex with a loop.
