This paper proposes a reformulation of the dual of the entropy-regularized optimal transport problem that makes it amenable to screening techniques. These techniques may lead to reduced dimension of the problem, and thus reduced computational costs. Two screening techniques are proposed, either using a fixed threshold or a fixed budget, and a theoretical error analysis is presented. The post-rebuttal consensus view among the reviewers is positive, and this paper is a good addition to the growing literature on computational optimal transport.