I'm not all at suprised by the statements that T C-T is good company or pleasant to be with (when it suits her) ...she'd be carp at getting support etc if she wasn't, goes with the territory etc,.
Ms TC-T could issue an apology for causing offence regarding the use of a non-entitled flying badge and desist from wearing them again. That would be enough for me.
By her own admission she has made several comments about how decades ago in common with other women she wasn't allowed to do a course that would lead to the award of the brevet... so she's either snuck off and done a "wings" course in secret somewhere (being supposedly taught to fly warbirds by ex mil QFIs doesn't count but I know most people here know that) or she's being a Walt.
I'd suggest she issues a full and frank statement over why she feels entitled to wear them or she stops wearing them.