Do we need a check valve for irrigation?

If your irrigation system uses a pressure tank, then yes. A check valve is necessary when pumping into any pressurized system. Pressure is required to propel the water, even in drip irrigation. If there is enough pressure to push water out, there is enough pressure to push back when you release the pump lever. This is what the check valve prevents. If you are using a gravity-fed irrigation system, a check valve would be needed if you are pumping to a tank more than 20 feet above the well.