Graph Neural Network (GNN) research has produced strategies to modify a graph's edges using gradients from a trained GNN, with the goal of network design. However, the factors which govern gradient-based editing are understudied, obscuring why edges are chosen and if edits are grounded in an edge's importance. Thus, we begin by analyzing the gradient computation in previous works, elucidating the factors that influence edits and highlighting the potential over-reliance on structural properties. Specifically, we find that edges can achieve high gradients due to structural biases, rather than importance, leading to erroneous edits when the factors are unrelated to the design task. To improve editing, we propose ORE, an iterative editing method that (a) edits the highest scoring edges and (b) re-embeds the edited graph to refresh gradients, leading to less biased edge choices. We empirically study ORE through a set of proposed design tasks, each with an external validation method, demonstrating that ORE improves upon previous methods by up to 50%.