Regarding intelligent transportation systems, low-bitrate transmission via lossy point cloud compression is vital for facilitating real-time collaborative perception among connected agents, such as vehicles and infrastructures, under restricted bandwidth. In existing compression transmission systems, the sender lossily compresses point coordinates and reflectance to generate a transmission code stream, which faces transmission burdens from reflectance encoding and limited detection robustness due to information loss. To address these issues, this paper proposes a 3D object detection framework with reflectance prediction-based knowledge distillation (RPKD). We compress point coordinates while discarding reflectance during low-bitrate transmission, and feed the decoded non-reflectance compressed point clouds into a student detector. The discarded reflectance is then reconstructed by a geometry-based reflectance prediction (RP) module within the student detector for precise detection. A teacher detector with the same structure as the student detector is designed for performing reflectance knowledge distillation (RKD) and detection knowledge distillation (DKD) from raw to compressed point clouds. Our cross-source distillation training strategy (CDTS) equips the student detector with robustness to low-quality compressed data while preserving the accuracy benefits of raw data through transferred distillation knowledge. Experimental results on the KITTI and DAIR-V2X-V datasets demonstrate that our method can boost detection accuracy for compressed point clouds across multiple code rates. We will release the code publicly at https://github.com/HaoJing-SX/RPKD.