Galaxy properties primarily depend on their host halo mass. Halo mass, in turn, depends on the cosmic web environment. We explore if the effect of the cosmic web on galaxy properties is entirely transitive via host halo mass, or if the cosmic web has an effect independent of mass. The secondary galaxy bias, sometimes referred to as “galaxy assembly bias”, is the beyond-mass component of the galaxy-halo connection. We investigate the link between the cosmic web environment and the secondary galaxy bias in simulations. First, we examine the extent to which the secondary galaxy bias can be accounted for with a measure of the environment as a secondary halo property. We find that the total secondary galaxy bias preferentially places galaxies in more strongly clustered haloes. In particular, haloes at fixed mass tend to host more galaxies when they are more strongly associated with nodes or filaments. This tendency accounts for a significant portion, but not the entirety, of the total secondary galaxy bias effect. Second, we quantify how the secondary galaxy bias behaves differently depending on the host halo proximity to nodes and filaments. We find that the total secondary galaxy bias is relatively stronger in haloes more associated with nodes or filaments.