What is the quality of the growl? Is it a serious "back the heck off or I will bite" or is it a playful growl. Yes there is a difference.
My Labrador sounds VICIOUS when she is on a tug or chewing a bone. But she is relaxed and happy. Just a talker. I don't correct it. It's just her.
If your girl is tensing up, preparing for a fight in regards to the toy, it needs to be corrected. I would not recommend a prong. I would teach her that good things happen when you pet her and she has a toy. So, to start I would not be touching her or the toy, I would just approach, say "goog girl" and offer something yummy. Once she is expecting something good as you approach, then lightly pet her,once , and then offer the treat. Slowly build this up so that she associates you with only good, no matter what she has. I would not, for a long time, invade her space, try to take the toy, anything like that. In fact I never do that. Unless she is chewing on something bad. You just want her to feel that your presence is always bringing good things.
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