Cloud-based serverless computing is an increasingly popular computing paradigm. In this paradigm, different services have diverse computing requirements that justify deploying an inconsistently Heterogeneous Computing (HC) system to efficiently process them. In an inconsistently HC system, each task needed for a given service, potentially exhibits different execution times on each type of machine. An ideal resource allocation system must be aware of such uncertainties in execution times and be robust against them, so that Quality of Service (QoS) requirements of users are met. This research aims to maximize the robustness of an HC system utilized to offer a serverless computing system, particularly when the system is oversubscribed. Our strategy to maximize robustness is to develop a task pruning mechanism that can be added to existing task-mapping heuristics without altering them. Pruning tasks with a low probability of meeting their deadlines improves the likelihood of other tasks meeting their deadlines, thereby increasing system robustness and overall QoS. To evaluate the impact of the pruning mechanism, we examine it on various configurations of heterogeneous and homogeneous computing systems. Evaluation results indicate a considerable improvement (up to 35%) in the system robustness.