As you can see from the screenshot, the Alpha Threshold (even with optimal settings) is not a good solution.
That was the first thing i tried. It does not solve the problem in a proper way, as the alpha threshold "eats" the pixels so the outline goes away along with the smooth transparency. The result is a very jagged hair, definitely not suitable for an high quality render.
Thank you for your feedback. Please try to select the Alpha Threshold of the hair mesh, the outline should be gone. Please let us know if it works. Reallusion