In multi-task adversarial networks, the accurate estimation of unknown parameters in a distributed algorithm is hindered by attacked nodes or links. To tackle this challenge, this brief proposes a low-communication resilient distributed estimation algorithm. First, a node selection strategy based on reputation is introduced that allows nodes to communicate with more reliable subset of neighbors. Subsequently, to discern trustworthy intermediate estimates, the Weighted Support Vector Data Description (W-SVDD) model is employed to train the memory data. This trained model contributes to reinforce the resilience of the distributed estimation process against the impact of attacked nodes or links. Additionally, an event-triggered mechanism is introduced to minimize ineffective updates to the W-SVDD model, and a suitable threshold is derived based on assumptions. The convergence of the algorithm is analyzed. Finally, simulation results demonstrate that the proposed algorithm achieves superior performance with less communication cost compared to other algorithms.