Do not confuse a neutral wire with a safety ground wire. A 240V GFCI usually has to be connected to the neutral wire of the source cable/line, coming from the breaker panel, to be able to supply the neutral to the load if it requires one, as was described above. If the load does not need a neutral - because it does not have any 120 volt devices such as time-clocks, programmers, etc. - then no neutral wire needs to be run to the load.
However a GFCI needs to have a ground wire from the source so that it can operate correctly to detect fault currents flowing into the safety ground wire coming from the load.
Note that the modern GFCI's other main way of detecting faults is to detect a sufficient difference - usually a difference of only about 30 milliamps - between the current flowing in one "hot" (for example a black wire) compared to the current flowing in the other "hot" (for example a red wire). Such a difference or imbalance must be caused by a leakage current going from one of the hots to ground without going through the protective ground wire: for example from a damp control switch that has cracked plastic insulation to a person's hand and then through his or her body to the damp floor in a kitchen or utility room.