With a Grey that talks, consistency, context and repetitiveness is key in teaching the bird new words. Chance picks up some words very quickly, but other words take time for her to understand and then speak. I think the bird needs to hear it spoken but also the context in which the word is spoken. For example, Chance finally started to say "eat" after years of me trying to get her to speak it. When we are cooking, and she smells the food, she starts saying "Eat, eeeeeeeat. Eat" because she understands the abstract meaning of the word... and wants to eat
Another thing she has learned is "Mmmm!" when she is offered food she will say "Mmm!" before accepting it. She has heard me say this when offering food to her but she also sees me say it before I eat something tasty ...I am a foodie and it's just amazing that she picked "Mmmm!" up the way she has, it's so cute, too.
I'm still working on "Buongiorno" when I wake her in the morning. She says "Goodnight" at bedtime but I am saying "buongiorno" to my spouse in the morning, also for her to see, too, so she gets the context.
So... just from experience, consistency, repetitiveness, and context all help in teaching a Grey to speak.