  We provide an explicit isomorphism between a quotient of the Bannai--Ito
algebra and the Brauer algebra. We clarify also the connection with the action
of the Lie superalgebra osp(1|2) on the threefold tensor product of its
fundamental representation. Finally, a conjecture is proposed to describe the
centralizer of osp(1|2) acting on three copies of an arbitrary finite
irreducible representation in terms of a quotient of the Bannai-Ito algebra.
