Graph network-based simulators (GNS) have demonstrated strong potential for learning particle-based physics (such as fluids, deformable solids, and granular flows) while generalizing to unseen geometries due to their inherent inductive biases. However, existing models are typically trained for a single material type and fail to generalize across distinct constitutive behaviors, limiting their applicability in real-world engineering settings. Using granular flows as a running example, we propose a parameter-efficient conditioning mechanism that makes the GNS model adaptive to material parameters. We identify that sensitivity to material properties is concentrated in the early message-passing (MP) layers, a finding we link to the local nature of constitutive models (e.g., Mohr-Coulomb) and their effects on information propagation. We empirically validate this by showing that fine-tuning only the first few (1-5) of 10 MP layers of a pretrained model achieves comparable test performance as compared to fine-tuning the entire network. Building on this insight, we propose a parameter-efficient Feature-wise Linear Modulation (FiLM) conditioning mechanism designed to specifically target these early layers. This approach produces accurate long-term rollouts on unseen, interpolated, or moderately extrapolated values (e.g., up to 2.5 degrees for friction angle and 0.25 kPa for cohesion) when trained exclusively on as few as 12 short simulation trajectories from new materials, representing a 5-fold data reduction compared to a baseline multi-task learning method. Finally, we validate the model's utility by applying it to an inverse problem, successfully identifying unknown cohesion parameters from trajectory data. This approach enables the use of GNS in inverse design and closed-loop control tasks where material properties are treated as design variables.