I really hope that this is a joke ask…
Tore it up or ate it whole? I fail to see how a dog could eat an entire cane-like branch. Unless if it was more the size of a small wand.
Either break it up and bury it, hopefully deep in the woods and far away from a house, or break it up and burn it.
And if it was indeed a proper blasting rod, keep check on that dog. Maybe perform some anti-witchcraft charms…
Apparently you have never owned an Alaskan Malamute.
Incomplete list of things my dog has eaten: Entire plastic jar of peanut butter (including half of the jar), multiple clothespins, a fidget spinner, an entire glove, a wooden knife handle, 3 lbs of gummi bears, a twelve inch hole in my bed.
A wand? No problem. But strangely she leaves my magick stuff alone, even offerings I leave for my ancestors.
I occasionally refer to her as the Wolf of Ragnarok because one day she will probably swallow the Sun and/or Moon.