Should I worry about a small piece of wood behind my dogs gums?

My sister, and brother in law were over working on something outside. Mu dog wanted to spend time with them, so they said it's fine, and they'll keep an eye on her. Well, I went out, and noticed my dog was chewing on a stick. Just now I noticed a very small piece behind her gum. It's probably the size... show more My sister, and brother in law were over working on something outside. Mu dog wanted to spend time with them, so they said it's fine, and they'll keep an eye on her. Well, I went out, and noticed my dog was chewing on a stick. Just now I noticed a very small piece behind her gum. It's probably the size of a flea. Maybe smaller. Shes gotten things stuck in her gums before, but I'm usually able to take my fingernail, and drag it out by the end, but this ones too deep. I was trying to get it out, but her gum was getting irritated, and started to bleed. Do you think the tissue will eventually push it out, or should I take more jurassic measures. I've had stuff stuck in my gums before, and ended up fine. Dont know if it's the same things with dogs though. It's not causing her any discomfort right now. I doubt she has any idea anything's there.
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