Standard Veronese degree and star configurations

We show that the standard Veronese degree of the defining ideal $I_{n,h}$ of a monomial star configuration is $\text{lcm}(1,2,\dots ,h)$, proving a conjecture by Grifo and Seceleanu. We also provide a counter-example for their question regarding upper bounds for the standard Veronese degree of monomial ideals.