Mesoscopic numerical simulations provide a unique approach for the quantification of the chemical influences on red blood cell functionalities. The transport Dissipative Particles Dynamics (tDPD) method can lead to such effective multiscale simulations due to its ability to simultaneously capture mesoscopic advection, diffusion, and reaction. In this paper, we present a GPU-accelerated red blood cell simulation package based on a tDPD adaptation of our red blood cell model, which can correctly recover the cell membrane viscosity, elasticity, bending stiffness, and cross-membrane chemical transport. The package essentially processes all computational workloads in parallel by GPU, and it incorporates multi-stream scheduling and non-blocking MPI communications to improve inter-node scalability. Our code is validated for accuracy and compared against the CPU counterpart for speed. Strong scaling and weak scaling are also presented to characterizes scalability. We observe a speedup of 10.1 on one GPU over all 16 cores within a single node, and a weak scaling efficiency of 91% across 256 nodes. The program enables quick-turnaround and high-throughput numerical simulations for investigating chemical-driven red blood cell phenomena and disorders.