Subtleties of Quantum Lefshetz without Convexity

Let $Y{}_{\theta }G$ be a complete intersection in a GIT quotient $X{}_{\theta }G$ cut out by a $G$-representation $E$. We show that the $E$-twisted quasimap $I$-function recovers invariants of $(Y,G,\theta )$ if its nonequivariant limit exists before restriction to $Y{}_{\theta }G$. This corrects a conjecture credited to Coates-Corti-Iritani-Tseng. We explain how to correct computations in the literature based on the faulty conjecture.