I think they just want something, anything in law that accepts some men really are women.
They had it with the GRA but FWS re-established that it's a legal fiction ith absolute limits, so now they need to re-establish a beachhead.
It doesn't matter how small and slight it is, it's crossing the barrier.
Once the law accepts that full, non qualified womanhood can be something other than natally female, they can chip away at the criteria to widen it.
And with an arbitrary line, which any non sex based line is going to be, it will always be possible to show how unfair it is that two people who are in almost identical situations face have very different outcomes just because they fall on different sides of a barrier that was arbitrarily determined and could so easily be moved just that little bit over.
They did it once by bypassing legal blessing and moving the men/women social barrier in practice further and further into the realm of men through media and insitutional capture. FWS stopped that.
So I think they are now trying to replay the same tactic with the law that blocked them and try to get well meaning judges to move specific provisions from the non arbitrary sex line onto an arbitrary gender line that is far more vulnerable to challenge (for good reason - TRAs can entirely reasonably and convinceingly demonstrate any given gender line is artbitrary and unjustified becsuse fundamentally, it is. Their dishonesty is the claim that the new gender line is any less so.)