Nonvanishing of the cusp differential in cohomology of Bianchi groups

Let $\Gamma_s$ be the stabilizer of a singular cusp $s$, let $M$ be a coefficient module as above, and let $d_2^{0,1}$ be the differential in the spectral sequence computing $H^2(\Gamma,M)$. The restriction of this differential to the summand associated with $s$ is a map

$$H^1(\Gamma_s,M)\longrightarrow E_2^{2,0}.$$

Nonvanishing conjecture. This restricted differential is nonzero.

This nonvanishing would determine the contribution of singular cusps to the computation of $H^2(\Gamma,M)$ by showing that the corresponding $E_2^{0,1}$ contribution is not killed trivially. The source reports considerable computational evidence, but does not establish the claim in general.