Functionally similar pathways are often seen in biological systems, forming feed-forward controls. The robustness in network motifs such as feed-forward loops (FFLs) has been reported previously. In this work, we studied noise propagation in a development network that has multiple interlinked FFLs. A FFL has the potential of asymmetric noise-filtering (i.e., it works at either the "ON" or the "OFF" state in the target gene). With multiple, interlinked FFLs, we show that the propagated noises are largely filtered regardless of the states in the input genes. The noise-filtering property of an interlinked FFL can be largely derived from that of the individual FFLs, and with interlinked FFLs, it is possible to filter noises in both "ON" and "OFF" states in the output. We demonstrated the noise filtering effect in the developmental regulatory network of Caenorhabditis elegans that controls the timing of distal tip cell (DTC) migration. The roles of positive feedback loops involving blmp-1 and the degradation regulation of DRE-1 also studied. Our analyses allow for better inference from network structures to noise-filtering properties, and provide insights into the mechanisms behind the precise DTC migration controls in space and time.