How much does it cost to deal with woodpeckers are destroying my tree?

The damage itself is not a billable repair; there is nothing to patch or fill. What you pay for is the diagnosis behind it — an inspection visit, plus possibly a decay measurement at the excavated area. If the answer is ash borer, cost shifts entirely into the treat-or-remove decision. If the answer is sapsucker, expect the trip charge and nothing more. Insist on being told which of the three patterns you have before agreeing to any work, because the recommended job differs enormously between them.