If someone says something that pushes your buttons, there's a part of you that buys into what they're saying, or it wouldn't bug you.
You asked how to "cope," and you've received some good advice here so far for coping. But why not move past mere coping and into Mastery?
If Georgia overtly attacks your competence and you are injured by that attack, boldly look for your own inner truth: how is Georgia correct? In what area am I incompetent? Maybe I'm incompetent in the literal sense she's talking about, or maybe my incompetence is a bit deeper -- maybe I haven't been competent in my communication or social skills or self-promotion, etc. When you have found incompetence (and if you look, you can), nod and thank Georgia. If you really want to take on mastery in a big way, ask Georgia to help you! "Hey, Georgia, I hadn't looked at it from your perspective; thanks for sharing that. How would you handle this situation?" She'll be disarmed -- she will no longer have a weapon with which to hurt you. You will have transformed an enemy into an ally.
If you just can't get your ego around that, simply smile and thank her for her input and tell her you'll take it under advisement.
And later, if it still rankles (you have revenge fantasies, for instance, or find yourself obsessing over what you *should* have said), that's your clue that you really would benefit from taking what was said under advisement -- you'll have a big clue that what she has said is a huge button for you, and huge buttons are huge opportunities for you to see something new about your own limiting beliefs -- and being free!