The diminished Sombor index of a graph \( G \) is defined by \[ \mathrm{DSO}(G) = \sum_{v_i v_j \in E(G)} \frac{\sqrt{d_i^2 + d_j^2}}{d_i + d_j}, \] where \( d_i \) and \( d_j \) denote the degrees of vertices \( v_i \) and \( v_j \), respectively. Very recently, Movahedi et al. [Diminished Sombor Index, MATCH Commun. Math. Comput. Chem. 95 (2026) 141-162] conjectured that among all tricyclic graphs, the minimum value of the diminished Sombor index is attained by the graph formed by connecting two disjoint cycles with two edges to form a quadrangle.

In this paper, we first demonstrate that this conjecture does not hold. We then determine the graph with the minimum diminished Sombor index within a specific class of tricyclic graphs, thereby providing a corrected characterization of extremal structures in this context.