If her cage is located near a popular doorway, I'd first move it to a less trafficked area of your house. Perhaps partially drape the back of the cage to give her a comfort area.
If you open her cage to pick her up and she freaks, then take a few steps back. Actually you might need to return to square one. Baby steps towards approaching her. Read her queues. If she becomes anxious, then step back to where she shows signs of comfort. With greys, it's all about doing exactly what they're asking of their people. It's not about what we want. If we follow what we'd like to have happen vs what the grey is trying to convey, then valuable progress will be lost.
I have a severely neglected rescue CAG who lived in an outside shack for 8 years. No handling whatsoever. It took me 2 months of working with him slowly. Now he does the mating dance and will step up. Unfortunately he was cage bound for such a long time that if I take a few steps away from his cage I can detect an increase in anxiety in him. So I stand or sit near his cage and everything's going great! Now I'm moving my chair or myself a step back to increase his tolerance of being away from his domain, monitoring his queues in real time, if you will.
If your grey has experience mistreatment in the past, you must first earn her trust. Patience is absolutely everything when it comes to greys!