Final answer:
Credit cards are most susceptible to damage from permanent magnets because they store data on magnetic strips, which can be corrupted or erased by strong magnetic fields.
Step-by-step explanation:
The item most susceptible to damage from permanent magnets is Credit cards. Credit cards contain magnetic strips that store data through magnetization. If exposed to a strong magnetic field, such as that of a permanent magnet, this information can be corrupted or erased. Cellular telephone antennas, polarized power connectors, and AA batteries do not rely on magnetic storage and are considerably less susceptible to magnetic fields when it comes to damage or interference.
In the context of interference with compass readings, DC current when you start your car is more likely to cause interference compared to AC current in your refrigerator. That's due to the transient magnetic field produced by the surge of DC current affecting the compass needle's alignment with Earth's magnetic field.