I believe the answer is: the Root-Takahira Agreement
In the Root-Takahira Agreement, The united states government agreed to let go of American influence in China and not intervene in Japanese's effort to invade China. In return, the Japanese government had to hand over Philippines' territory to united states.
The correct answer for the given question above would be the first option. The Gentlemen's Agreement is the agreement that would prevent Japanese intervention in its neighboring island of the Philippines. The Gentlemen's Agreement is an agreement that is not written and only supported by the integrity of the counterpart to actually abide by the terms of the agreement.
