Recently, Ebrahimi et al. [C*-convexity and C*-faces in *-rings, Turk. J. Math. 36 (2012), 131--145] identified the optimal points of continuous unital homomorphisms on some C*-convex sets of a topological *-ring. In this short note, we generalize their results for continuous (non-unital) homomorphisms in a topological *-ring. Moreover, for continuous unital homomorphisms, we point out the same conclusion does not hold everywhere that a Krein-Milman type theorem exists. An important issue is so that we do not assume that homomorphisms are unital.