The "good neighbor" polices of the 1920s and 1930s saw the United States permanently remove all its troops from Latin America.

false

Explanation:

This statement is false

Franklin Roosevelt administration designed The Good Neighbour policy, as a way to improve relationships with Latin American governments at times where the world was just about to come to international conflict (prior to world war II)

This means that cooperation agreements and trade were stimulated in order to keep geopolitical stability in the region of Latin America.

However:

The outburst of the Mexican Revolution, and the so-called Banana Wars, among other significant conflicts, mean that American military presence in the South of the Continent was to remain.