The Web of Things (WoT) enhances interoperability across web-based and ubiquitous computing platforms while complementing existing IoT standards. The multimodal Federated Learning (FL) paradigm has been introduced to enhance WoT by enabling the fusion of multi-source mobile sensing data while preserving privacy. However, a key challenge in mobile sensing systems using multimodal FL is modality incompleteness, where some modalities may be unavailable or only partially captured, potentially degrading the system's performance and reliability. Current multimodal FL frameworks typically train multiple unimodal FL subsystems or apply interpolation techniques on the node side to approximate missing modalities. However, these approaches overlook the shared latent feature space among incomplete modalities across different nodes and fail to discriminate against low-quality nodes. To address this gap, we present FedMobile, a new knowledge contribution-aware multimodal FL framework designed for robust learning despite missing modalities. FedMobile prioritizes local-to-global knowledge transfer, leveraging cross-node multimodal feature information to reconstruct missing features. It also enhances system performance and resilience to modality heterogeneity through rigorous node contribution assessments and knowledge contribution-aware aggregation rules. Empirical evaluations on five widely recognized multimodal benchmark datasets demonstrate that FedMobile maintains robust learning even when up to 90% of modality information is missing or when data from two modalities are randomly missing, outperforming state-of-the-art baselines.