Purpose: Scatter artifacts drastically degrade the image quality of cone-beam computed tomography (CBCT) scans. Although deep learning-based methods show promise in estimating scatter from CBCT measurements, their deployment in mobile CBCT systems or edge devices is still limited due to the large memory footprint of the networks. This study addresses the issue by applying networks at varying resolutions and suggesting an optimal one, based on speed and accuracy. Methods: First, the reconstruction error in down-up sampling of CBCT scatter signal was examined at six resolutions by comparing four interpolation methods. Next, a recent state-of-the-art method was trained across five image resolutions and evaluated for the reductions in floating-point operations (FLOPs), inference times, and GPU memory requirements. Results: Reducing the input size and network parameters achieved a 78-fold reduction in FLOPs compared to the baseline method, while maintaining comarable performance in terms of mean-absolute-percentage-error (MAPE) and mean-square-error (MSE). Specifically, the MAPE decreased to 3.85% compared to 4.42%, and the MSE decreased to 1.34 \times 10^{-2} compared to 2.01 \times 10^{-2}. Inference time and GPU memory usage were reduced by factors of 16 and 12, respectively. Further experiments comparing scatter-corrected reconstructions on a large, simulated dataset and real CBCT scans from water and Sedentex CT phantoms clearly demonstrated the robustness of our method. Conclusion: This study highlights the underappreciated role of downsampling in deep learning-based scatter estimation. The substantial reduction in FLOPs and GPU memory requirements achieved by our method enables scatter correction in resource-constrained environments, such as mobile CBCT and edge devices.