You could frost the lower panes of glass to prevent them from interacting.
There’s spray on snow decoration for windows, or a spray from Rustoleum for frosting glass, or you could use an cling vinyl wrap. Probably under $20 for more product than you will need for this door. They make some of the vinyl wraps that look like stained glass. You just cut them to size and stick them on. Both the spray and vinyl options also come off easily when you re ready to try giving her the window back.

I’ve had neighborhood cats swing by to spray or pick fights through glass doors like this, and from my perspective it’s the cat outside the house that’s causing the issue here.