The answer is in the same card of the SBVD, there you can read the following:
"The SBVD recovers Obedience in the same way characters recovers fatigue and stress, using the owner's Animal Handling instead of Discipline or Resilience."
Therefore, the SBVD recovers automatically an amount of Obedience at the end of any encounter equal to the owners Fel. Additionally, during a rally step it recovers 1 point of Obedience, and it's owner can attempt an Easy (1d) Animal Handling check to recover 1 Obedience per Hammer generated (this of course counts towards the actions the PC can perform during the rally step). Finally, with an overnight rest the SBVD will recover an amount of Obedience equal to the owner's Fel.