Diode Parallel to a DC Contactor

..."When the power supply is connected to the relay, the inductance coil’s voltage builds up to match that of the power source. The speed at which current can change in an inductor is limited by its time constant. In this case, the time it takes to minimize current flow through the coil is longer than the time it takes for the power supply to be removed. Upon disconnection, the inductance coil reverses its polarity in an attempt to keep current flowing according to its dissipation curve (i.e., % of maximum current flow with respect to time). This causes a huge voltage potential to build up on the open junctions of the component that controls the relay.

This voltage built up is called flyback voltage. It can result in an electrical arc and damage the components controlling the relay. It can also introduce electrical noise that can couple into adjacent signals or power connections and cause microcontrollers to crash or reset. If you have an electronics control panel that resets each time a relay is de-energized, it’s highly possible you have an issue with flyback voltage.

To mitigate this issue, a diode is connected with reverse polarity to the power supply. Placing a diode across a relay coil passes the back EMF and its current through the diode when the relay is energized as the back EMF drives the flyback protection diode in forward bias. When the power supply is removed, the voltage polarity on the coil is inverted, and a current loop forms between the relay coil and protection diode; the diode again becomes forward biased. The diode allows current to pass with minimal resistance and prevents flyback voltage from building up, hence the name flyback diode."...

https://resources.altium.com/bill-of-materials-blog/why-you-should-use-a-flyback-diode-in-a-relay-to-prevent-electrical-noise-in-your-circuits

The purpose of the diode is to act as a shunt when the coil is disconnected from the supply. Normally the diode is reverse biased as shown in the connection but when the coil is opened the collapsing magnetic field generates a reverse polarity voltage which the diode shunts. Depending on the type of diode used it will conduct between 0.2V for a Shottke and 0.6V for a silicon diode.

If the diode is not used then the reverse voltage spike is impressed across the switching element which can be solid state, relay contacts, switch mechanism anything to control power to the coil.

If the DI/DT change in current over change in time is very high sometimes a resistor is used in series with the diode however the coil may hold in for slightly longer due to the time constant of the inductance, capacitance of the coil and the resistor value.

Resistors can be used but they consume power and generate heat because they shunt the coil supply under normal operating conditions.

MOVs require a certain voltage to begin conducting and if you choose to use one of them then the conduction point needs to be high enough not to conduct under normal supply conditions but low enough to shunt too high a reverse voltage before damage can occur to other equipment.