We report on a spectroscopic analysis of the X-ray emission from IGR J17062-6143 in the aftermath of its 2020 June intermediate duration Type I X-ray burst. Using the Neutron Star Interior Composition Explorer, we started observing the source 3 hr after the burst was detected with the Monitor of All-sky X-ray Image Gas Slit Camera, and monitored the source for the subsequent 12 days. We observed the tail end of the X-ray burst-cooling phase, and find that the X-ray flux is severely depressed relative to its historic value for a three-day period directly following the burst. We interpret this intensity dip as the inner accretion disk gradually restoring itself after being perturbed by the burst irradiation. Superimposed on this trend we observed a 1.5 day interval during which the X-ray flux is sharply lower than the wider trend. This drop in flux could be isolated to the nonthermal components in the energy spectrum, suggesting that it may be caused by an evolving corona. Additionally, we detected a 3.4 keV absorption line at 6.3σ significance in a single 472 s observation while the burst emission was still bright. We tentatively identify the line as a gravitationally redshifted absorption line from burning ashes on the stellar surface, possibly associated with 40Ca or 44Ti.