The name of the app is FluidMask. It’s a one trick pony. It only removes backgrounds. When used to the max it can even remove smoke from a background. You can make hard edges with it, but you can also feather the edges so the result is a transition, not an edge. I’ve used the Mac version lightly for years.
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Actually, for a simple image as described by the OP you can use Keynote for iOS. Load the image in a Keynote slide, select the image and choose instant alpha. Select the grey region and tap and drag to widen the acceptance range of grey levels. Deselect then select again to get an option to copy it. Now you can paste the modified image where you like.