George Floyd 's brother Terrence is going in on Lil Yachty for referencing George's death in a new song ... and Terrence says Yachty needs a history lesson.

Terrence joined us on "TMZ Live" Friday, and we asked how he felt about Lil Yachty's new song with the lyrics, "Put my knee up on her neck, I went George Floyd."

George's brother says Lil Yachty and others should be careful what they say about GF ... because his death remains a sensitive topic, and it still hurts and upsets the family. Gallery Launch Gallery

Terrence says Lil Yachty must not have been paying attention in 2020 and 2021 when George's death set off a wave of protests across the world ... and he feels the lyrics show Yachty doesn't have his finger on the pulse of the culture.

As you know ... Floyd died du

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