The effect is optional, and activates when "Amazoness Chain Master" is sent from the field to the Graveyard when destroyed by battle.
Previously Official Rulings
These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
The effect of “Amazoness Chain Master” is optional. You choose whether or not to activate it when this monster is destroyed as a result of battle and sent to the Graveyard.
If you have your opponent’s monster that you acquired with “Amazoness Chain Master”, and your opponent activates “Disturbance Strategy”, the monster returns to the owner’s Deck. However, you draw the same number of cards that you had in your hand, including 1 card for the monster you acquired with “Amazoness Chain Master”.
If you acquired your opponent’s monster with “Amazoness Chain Master”, and “Remove Brainwashing” is activated, the monster returns to the original owner if it is on the field. However, if it’s still in your hand then it is not returned.