This plug-in is more like an equation, where one plays with numbers, and less like an intuitive user interface doing specific adjustments. I played with the values some and was able to reduce the faint ringing. The stronger ringing apparently is considered as picture and nothing much happens there. But some improvement is better than none ... except that there is a slight softening effect. (This plug-in is in "alpha" and has been that way for years.)

Here is a before (left) & after (right). Zoom-in to examine the result of ..
DeHalo_alpha( rx=3, ry=1, darkstr=0.4, lowsens=25, highsens=75 )
** note: ry=1 performs no work on the y-axis (vertical) **