Here is one of my trees. It is a ficus. you can see that it has bite marks of varying depth. This is so because the wire had more pressure on the parts that I bent.
See the wire on this branch? It's flush with the branch. That means that the branch has grown around the wire and is pretty deep. It shouldn't get this deep. Still this is a ficus so in a month it'll grow back and there'll be some discoloration and in two months after that will be gone. To safely remove the wire i used a pair of wire cutters. Snip along the branch try to cut the wire along the same line. This will make removing the wire easier. You should be able to remove the wire with gentle pressure. If the bit of wire does not come off then cut it at the halfway point.
This is another branch. you can see that it also has wires scarring. I had to rewire it, but if you notice I wrapped it around the other way so the wire wouldn't fill the scars in.
So in conclusion for Slow growing trees you do not want to bite the branch. Fast growing trees you want to have some bite to make sure that the branch is set.
Oh, by the way. This ficus was an epiphyte the grounds keepers hacked last year. When I collected it, it had no branches or leaves. Now it has amazing huge leaves and it is developing branches. I just noticed from the picture above that it is time to remove the dead wood and give it a nice smooth and tapered look. Cheers.
Update March 30
Twenty seven days after I removed the wire the tree is healing nicely.
One more month and the wire scars will be all but gone.