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Coarse-grained molecular dynamics (CGMD) simulations address lengthscales and timescales that are critical to many chemical and material applications. Nevertheless, contemporary CGMD modeling is relatively bespoke and there are no black-box CGMD methodologies available that could play a comparable role in discovery applications that density functional theory plays for electronic structure. This gap might be filled by machine learning (ML)-based CGMD potentials that simplify model development, but these methods are still in their early stages and have yet to demonstrate a significant advantage over existing physics-based CGMD methods. Here, we explore the potential of Δ-learning models to leverage the advantages of these two approaches. This is implemented by using ML-based potentials to learn the difference between the target CGMD variable and the predictions of physics-based potentials. The Δ-models are benchmarked against the baseline models in reproducing on-target and off-target atomistic properties as a function of CG resolution, mapping operator, and system topology. The Δ-models outperform the reference ML-only CGMD models in nearly all scenarios. In several cases, the ML-only models manage to minimize training errors while still producing qualitatively incorrect dynamics, which is corrected by the Δ-models. Given their negligible added cost, Δ-models provide essentially free gains over their ML-only counterparts. Nevertheless, an unexpected finding is that neither the Δ-learning models nor the ML-only models significantly outperform the elementary pairwise models in reproducing atomistic properties. This fundamental failure is attributed to the relatively large irreducible force errors associated with coarse-graining that produces little benefit from using more complex potentials.