There are miles of acacia confusa where I live, and from what I've seen if you leave a tree with just a strip like that it will die about half of the time. I've come across large areas where people cut large strips from the trunks of several trees and many of them don't make it. I think having the core exposed to the air can make them sick. What I usually do is just find a good sized root and find a spot where it branches off under ground. Then I'll make a clean cut there and pull/dig it up and bury the wound. None of the trees I have harvested this way have died. Though if you want to be sure not to harm it the phyllodes work fine, about half potency but way easier to get.