Rich countries don't think much about poor countries.

Literal

Rich countries [topic-は] poor countries [possessive-の] matter [object-を] not-much thinking-[ていない]

The 'の こと' construction — literally 'the matter of poor countries' — is used to treat the poor-countries as a topic of thought rather than a direct object. A common pattern after verbs of mental action: ~のことを考える, ~のことを知る, ~のことが好きだ. あまり + negative = 'not much, not very'.