Illicit activities in the waste management network, such as waste laundering, misreporting, or trade of stolen waste pose serious environmental and regulatory challenges. Detecting these behaviours is challenging, because they often emerge from higher-order interactions among multiple entities, and are not continuous over time. Furthermore, these activities often manifest as triangles in the network, and the participation of individuals in these waste transfer structures is additionally suspicious. Traditional anomaly detection methods, which rely on first-order relationships or static analyses, struggle to capture these complex, temporally dynamic patterns. To address this challenge, we propose a Conditional Motif-Based Graph Convolutional Network (CM-GCN) that integrates condition-driven triangular motifs directly into the GCN message-passing mechanism. The CM–GCN learns structural embeddings that encode both local graph topology and node attributes–based connectivity to triangular motifs. To detect sudden or sporadic changes, these weekly embeddings are processed by a Long Short–Term Memory Variational Autoencoder (LSTM–VAE), which models temporal behaviour and identifies anomalies through spikes in reconstruction error. Experiments on one year of Portuguese waste transport data demonstrate that the proposed approach effectively highlights companies with known illicit behaviour. The CM–GCN–LSTM–VAE outperformed a standard GCN–LSTM–VAE that ignores motif structure. Results are comparable to, and slightly improve upon, an LSTM–VAE trained on a manually engineered triangle–based feature. This demonstrates that higher–order structural representations learned by the model provide a more informative signal, while simple pairwise relationships contribute little to the detection of complex behaviours.