  In this paper, we extend the Gribov-Zwanziger framework accounting for the
existence of Gribov copies to the mass deformed Bagger--Lambert--Gustavsson
(BLG) theory in $\mathcal{N} =1 $ superspace. The restriction of the domain of
integration in the Euclidean functional integral to the first Gribov horizon is
implemented, by adding a non-local horizon term to the effective action.
Furthermore, the soft breaking of the BRST symmetry due to horizon term is
restored with the help of external sources. We compute the various Ward
identities for this theory relying on the Lie 3-algebras.
