Stochastic simulations are used to study the linking properties of solutions of circular polymers in slit confinement. Specifically, we consider dispersions of semiflexible rings at various densities phi and slit height, H. The competing length scales in the system have significant effects on the interchain entanglement. We observe that the linking probability is largest for a specific slit height that is about independent of solution density. However, when phi is large, links with given number of components can significantly depart from the overall linking trend with H. In this case, binary links are found to be least probable when the overall incidence of links is maximum. We show that this intriguing dichotomy and other properties, including upper bounds on links abundance, can be quantitatively captured with an approximate model based on continuum percolation theory. Our results suggest that slit-like confinement could be used in applicative contexts to control independently both the average abundance and the topological complexity of annealed molecular links.