Paleoclimate records can be considered low-dimensional projections of the climate system that generated them. Understanding what these projections tell us about past climates and changes in their dynamics is the main goal of time series analysis on such records. Linear techniques provide insight into changes in the periodic behavior of the climate, but are intrinsically limited. Novel tools from nonlinear time series analysis allow us to examine changes in other kinds of behavior that are reflected in these records. Laplacian Eigenmaps of Recurrence Matrices (LERM) is one such technique, providing information about when fundamental shifts in climate dynamics have occurred. This is done by leveraging time delay embedding to construct a manifold that is mappable to the attractor of the climate system; this manifold can then be analyzed for significant dynamical transitions. Through numerical experiments with observed and synthetic data, LERM is applied to detect both gradual and abrupt regime transitions. Our paragon for gradual transitions is the Mid-Pleistocene Transition (MPT). We observe that LERM is robust in detecting gradual MPT-like transitions for sufficiently high signal-to-noise ratios, though it tends to occur towards the later stages of the transition. Our paragon of abrupt transitions is the 8.2ka event; we find that LERM is generally robust at detecting 8.2ka-like transitions for sufficiently high signal-to-noise ratios, though edge effects become more influential. We conclude that LERM can usefully detect dynamical transitions in paleogeoscientific time series. An associated Python package is proposed to ease its use in the fields of paleoclimatology and paleoceanography.