The resolution of surface-acquired magnetotelluric data is typically not sufficiently high enough in monitoring surveys to detect and quantify small resistivity variations produced within an anomalous structure at a given depth within the subsurface. To address this deficiency we present an approach, called "layer stripping", based on the analytical solution of the one-dimensional magnetotelluric problem to enhance the sensitivity of surface magnetotelluric responses to such subtle subsurface temporal variations in resistivity within e.g. reservoirs. Given a well-known geoelectrical baseline model of a reservoir site, the layer stripping approach aims to remove the effect of the upper, unchanging structures in order to simulate the time-varying magnetotelluric responses at depth. This methodology is suggested for monitoring all kinds of reservoirs, e.g. hydrocarbons, gas, geothermal, compress air storage, etc., but here we focus on CO2 geological storage. We study one-dimensional and three-dimensional resistivity variations in the reservoir layer and the feasibility of the method is appraised by evaluating the error of the approach and defining different detectability parameters. The geoelectrical baseline model of the Hontomín site (Spain) for CO2 geological storage in a deep saline aquifer is taken as our exemplar for studying the validity of the 1D assumption in a real scenario. We conclude that layer stripping could help detect resistivity variations and locate them in the space, showing potential to also sense unforeseen resistivity variations at all depths. The proposed approach constitutes an innovative contribution to take greater advantage of surface magnetotelluric data and to use the method as a cost-effective permanent monitoring technique in suitable geoelectrical scenarios