What you can do is gently tap the ends of the wire ring around to near one of the three mount holes. Then it is possible to lever (in that hole) against the wire ring so that the end is out of the groove a little. With that done, you can normally get something underneath the ring & then feed it underneath allowing the end to be gripped & pulled out.
It is far easier to do than write up how to do it, but I hope you can understand my attempt...
You’ll need thin screwdrivers, to hand, to get in to flick out the wire ring.
For what it’s worth, I used to modify discs to allow for clunking(!) but nowadays I always refit the anti rattle wire ring after cleaning up/polishing the surface of the hub & lightly Copa-slipping the surfaces. Nor do I increase the three holes size but apply the same techniques to ensure the disc can slide laterally on its mounts. My belief is that the disc will run truer with the intended clearance & therefore less likelihood of tipping/drag against the pads, even if it is only a nat's.....
