I couldn't care less about the woman.

我才不在乎那个女人呢。

《柯林斯英汉双解大词典》

They will care less about their own background.

他们不太关心自己的背景。

youdao

They couldnt care less about their parents.

他们一点也不关心他们的父母。

youdao

In that, there is another nugget: care less about the reputations of others as presented online.

FORBES: The Beauty of Never Forgetting

He could care less about the embattled middle-class UAW workers earning more than a hundred grand.

FORBES: Ohioans Are No Fools: Obama Did NOT Save Your Automotive Jobs (Update: Fact sheet at the end)

Syracuse, of course, couldn't care less about some Michigan team from two decades ago.

WSJ: Contrasting styles on display in Syracuse-Michigan