When providing task demonstrations to a remote robot over the network via bilateral teleoperation, communication impairments are unavoidable, hindering the human operator from delivering high-quality demonstrations. Poor-quality demonstrations can negatively impact the robot's ability to learn and generalize. In this letter, we propose to enhance learning performance by introducing a network-aware confidence weighting strategy for remote learning from demonstration. Our approach extends the Hidden Semi-Markov Model (HSMM) and its task-parameterized version (TP-HSMM) to their confidence-weighted versions, WHSMM and WTP-HSMM. We evaluated various weight metrics that serve as teleoperation transparency measures and demonstration quality indicators under varying communication delays. We validated the proposed approach in two different in-contact tasks using data collected from 18 participants. The results show that weighting improves task performance in reproduction by up to 42% in the force precision and 63% in the success rate, demonstrating the potential of the proposed approach to enhance the effectiveness of robot learning from remote demonstrations.