Question
Hi. I have a customer with a similar problem of holes in their bradford pear. The holes are almost perfect in size and shape and in concentric circles around the tree. is this a woodpecker? The damage seems almost too perfect in symmetry.

Answer
Sounds like sapsuckers wood peckers
Most woodpeckers rely on insects and tree sap as their primary sources of food. Many woodpeckers feed almost entirely on insects, finding a majority of them beneath the bark on dead tree limbs and in other situations where their feeding is considered beneficial. However, the yellow-bellied sapsucker relies on the sap of trees for over half of its food, with the balance of its diet consisting of insects, berries, and fruits.
The damage consists of rows of neatly spaced horizontal or vertical holes in tree trunks and branches. Rarely does the woodpecker kill a tree in this area, but its feeding may weaken the tree, making it more susceptible to secondary disease and insect problems.
Trees with thick bark (oak) are damaged little. Where as trees with thin bark (maple) can be damaged a great deal by the holes.
The sapsucker makes the holes and the tree produces a drop of sap in the hole--insects come to feed on the sap and the woodpecker returns to feed on the insects. There is not need to fill the holes-the tree will heal over these by themselves. To stop insects from coming and thus discourage the woodpecker from feeding I would spray the area with a insecticide. Something like malathion or sevin will kill the insects and the woodpeckers will leave.
Doing nothing is ok too since the trees health is not going to be damage.