  We study the $\mathcal{N}=6$ superconformal Chern-Simons matter field theory
(the ABJM theory) conformally coupled to a Lorentzian, curved background
spacetime. To support rigid supersymmetry, such backgrounds have to admit
twistor spinors. At the classical level, the symmetry of the theory can be
described by a conformal symmetry superalgebra. We show that the full
$\mathcal{N}=6$ superconformal algebra persists at the quantum level using the
BV-BRST method.
