The deployment of artificial intelligence in medical imaging is hindered by high computational complexity and resource-intensive processing of volumetric data. Although chest computed tomography (CT) volumes offer richer diagnostic information than projection radiography, their use in AI-based diagnosis remains limited due to the computational burden of processing uncompressed volumetric images (typically stored in NIfTI or DICOM format). Addressing the growing need for low-resource deployment and efficient electronic data transfer, we investigate the utilization of JPEG-compressed chest CT volumes for thoracic abnormality detection. We propose Feature Attention Style Transfer (FAST), a novel distillation framework that transfers both activation patterns and structural relationships from high-fidelity CT representations to a spatiotemporal visual encoder operating on compressed inputs. By combining Gram-matrix-based attention style preservation with dual-attention feature alignment, FAST enables robust feature extraction from degraded volumes. Furthermore, we introduce Structured Factorized Projection (SFP), leveraging Block Tensor Train decomposition as a parameter-efficient alternative to dense projection layers, reducing projection-head parameters by almost half. Our contrastive learning pipeline, CT-Lite, integrates these components with a SigLIP-based multimodal alignment objective. Experiments on CT-RATE, NIDCH, and Rad-ChestCT demonstrate that CT-Lite achieves AUROC within 5-7\% of the uncompressed-input baseline across all three datasets, despite operating on compressed inputs with significantly fewer parameters, paving the way for AI-based clinical evaluation under resource constraints.