  This paper reports the first differential measurement of the charged-current
$\overline{\nu}_{\mu}$ interaction cross section on water with no pions in the
final state. The unfolded flux-averaged measurement using the T2K off-axis near
detector is given in double differential bins of $\mu^+$ momentum and angle.
The integrated cross section in a restricted phase space is
$\sigma=\left(1.11\pm0.18\right)\times10^{-38}$ cm$^{2}$ per water molecule.
Comparisons with several nuclear models are also presented.
