Tactile teleoperation allows users to physically interact with the remote environment, and revolutionizes the set of new applications like remote surgical operation. Thus, it is sensitive to the reliability and end-to-end (E2E) latency including the sojourn latency, the transmission latency, and the computation latency. For reducing E2E latency and increasing reliability, the grant-free transmission with $K$-repetition and the mobile edge computing (MEC) are usually utilized. In this paper, we study the upper bounds of the tail-distribution function of the E2E latency in tactile teleoperation. First, we analyze the success probability of transmission, and formulate the statistical model of service process with consideration of the grant-free access, the $K$-repetition and the pilot collision. Then, based on martingales theory, the upper bounds of the tail-distribution of E2E latency are derived with joint consideration of the computation latency of MEC. Finally, the minimum E2E latency bound violation probability is obtained by allocating the latency budgets of uplink latency and MEC computation latency. Simulation results show that our theoretical analysis is accurate and the allocation is feasible.