  We establish the scattering of solutions to the focusing mass supercritical
nonlinear Schr\"odinger equation with a repulsive Dirac delta potential \[
i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in
{\mathbb R}\times{\mathbb R}, \] at the mass-energy threshold, namely, when
$E_{\gamma}(u_{0})[M(u_{0})]^{\sigma}=E_{0}(Q)[M(Q)]^{\sigma}$ where $u_{0}\in
H^{1}({\mathbb R})$ is the initial data, $Q$ is the ground state of the free
NLS on the real line ${\mathbb R}$, $E_{\gamma}$ is the energy, $M$ is the mass
and $\sigma=(p+3)/(p-5)$. We also prove failure of the uniform space-time
bounds at the mass-energy threshold.
