The compressor started clunking which continued for several seconds before it quieted down.

You disturbed the balance when you moved the running fridge. The clinking was the rotor in the compressor being moved out of its natural orbit. The fact that the noise subsided is a good thing. Remember that the compressor is a motor and pump assembly, suspended by springs in a metal container. If this happened while the compressor was running and with you moving the refrigerator, it could have been a domino effect that subsided after the movement of the refrigerator was completed, because some vibration occurs inside the compressor while it is running that is absorbed by the springs, but your movement of the refrigerator most likely amplified or increased this internal vibration. If the customer has not heard this noise prior to your movement of the refrigerator and it has not re-occurred I would deem it a normal situation. However if it does randomly occur then I would suspect one of the internal springs has stretched or broken and this would require replacement of the compressor to effect a repair. Most likely you will have no other issues with the unit.