It's probably just socialized to be transmisogynist by evil patriarchal comphet anti-queer dog media.

You need to challenge the dog's ontology of experience by introducing radical reading materials from bell hooks, Andrea Long Chu and other feminist thinkers and engaging in regular dialectic conversations if you want the dog to understand that trans women are women. I would also suggest keeping track of what websites the dog uses and what sort of other dogs they hang out with. Transphobia is insidious and is more prevalent among the dog parks than you would think. We need to combat dog bigotry wherever it occurs.

If all else fails, berate the dog regularly, call it ugly, jealous, sexually dysfunctional, and threaten to rape it or forcibly inject it with sterilizing hormones. I don't know how exactly this approach works but everyone does it so there must be a good reason.