Air Pump

If you mean the AIR pump that puts air into the exhaust system, the tick can be a bad check valve or internal pump damage. Hard to tell without hearing it up close.
As for removing it, you can BUT if you are in a state with emissions inspection it will fail, and I have seen more than once where removing the pump caused the catalytic converter to plug up because the extra air helps it to burn off the excess fuel. I would replace it with either a reman or a used pump.