How are microlensing events used to constrain the size of innermost stable circular orbits around spinning black holes? The third paragraph of the introduction to the ArXiv preprint Constraining Quasar Relativistic Reflection Regions and Spins with Microlensing says:

Quasar microlensing has significantly improved our understanding of the accretion disks (e.g., [five refs]) and non-thermal emission regions (e.g., [seven refs]) of quasars, and the demographics of microlenses in the lens galaxy (e.g., [three refs]) . Since the magnification diverges on the caustics produced by the lensing stars, quasar microlensing can constrain arbitrarily small emission regions if they can be isolated from other emission, in position, velocity, or energy. In particular, microlensing can be used to constrain the spin of black holes by measuring the ISCO size. (emphasis added)

ISCO was previously identified as innermost stable circular orbit.
From what I understand from Wikipedia's Gravitational microlensing; How it works, a microlensing observation records a short term brightening of an object due to focusing by an intervening gravitational body, without useful spatial resolution.
See also the Planetary Society's explanation Microlensing; Beyond our Cosmic Neighborhood
Question: How are microlensing events used to constrain the size of innermost stable circular orbits around spinning black holes? What instruments are used and what kind of analysis is done to obtain a ISCO constraint?



Example light curve of Gravitational Microlensing event - OGLE-2005-BLG-006 Source
I think most of the paper is devoted to describing how they do it.  (This may be more of a comment than an answer, because I'm an amateur and not prepared to go through the paper in detatil).

Note that microlensing here is a little different than microlensing as described in the Wikipedia.  In the Wikipedia page and the Planetary Society page you reference, microlensing refers to observing the change in brightness over time of a small, relatively nearby object when a closer but non-luminous object passes in front of it from our line-of-sight.  In this paper, microlensing refers to the extra magnification that can be provided to tiny sub-sections of a "macrolensed" (gravitationally-lensed cosmologically distant object) by the chance placement of a star at the right position in the lensing geometry.

The authors of the paper figure out how this sort of microlensing might apply to the innermost parts of a quasar, where it might highlight small parts of the accretion disk, and so the contribution of those parts to the spectrum (in this case, one particular X-ray emission line characteristic of active galactic nuclei accretion disks) of the "macrolensed" object as seen from Earth.  They apply a statistical model of the likelihood of such microlensing and how it would affect the measured spectrum of a range of possible active-galactic nuclei (resolving a particular part of the accretion disk with microlensing would enhance that particular parts contribution to the whole, and each part of the accretion disk would have a different relativistic shift of the emission line as it whips around the central black hole), and then see how their model matches the actual measured spectrum.  It sounds like they are operating at the limits of statistical significance-- at least for most of the objects in their study-- but got more robust data for one particular object.