We demonstrate that study of the evolving magnetic nature of coronal dimming regions can be used to probe the large-scale magnetic structure involved in the eruption of a coronal mass ejection (CME). We analyse the intensity evolution of coronal dimming regions using 195 Å data from the Extreme ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory (SOHO). We measure the magnetic flux, using data from the SOHO/Michelson Doppler Imager (MDI), in the regions that seem most likely to be related to plasma removal. Then, we compare these magnetic flux measurements to the flux in the associated magnetic cloud (MC). Here, we present our analysis of the well-studied event on 12 May 1997 that took place just after solar minimum in a simple magnetic configuration. We present a synthesis of results already published and propose that driven ``interchange reconnection'' between the expanding CME structure with ``open'' field lines of the northern coronal hole region led to the asymmetric temporal and spatial evolution of the two main dimming regions, associated with this event. As a result of this reconnection process, we find the southern-most dimming region to be the principal foot-point of the MC. The magnetic flux from this dimming region and that of the MC are found to be in close agreement within the same order of magnitude, 10²¹ Mx.