Moreover, the third paper you cited specifically singles out the OWLS-dependence of a parameter ($$\kappa_{tr}$$) as an explanation for why they can't put constraints on it. If the paper was referring to OWLS to begin with, this section would make no sense.
You obviously missed page 4, left column where they explain the limits on the RMS parameter $$\beta-\delta-1/2$$. In post 253 I already explained to you its significance. Do you remember it?
Not only that, you are looking at the wrong $$k$$ parameter, the parameter that constrains OWLS anisotropy is $$k_e$$ and $$k_o$$ (page 3. left column).