On Tuesday, the House passed a $40bn aid package to Ukraine. Every Democrat present voted for the legislation, while 57 Republicans voted against the package, including Ms Greene.
But the feud began when Mr Crenshaw, a Texas Republican who lost an eye while serving in Afghanistan, tweeted about how the Biden administration was supposedly letting drugs pour across the US-Mexico border.
In response, someone criticised him over his vote for the Ukraine package.
“Yeah, because investing in the destruction of our adversary’s military, without losing a single American troop, strikes me as a good idea,” he tweeted in response. “You should feel the same.”
In response, Ms Greene, who lost her personal Twitter account earlier this year, quote-tweeted Mr Crenshaw and said he didn’t care about Ukrainian lives.
“So you think we are funding a proxy war with Russia?” she said. “You speak as if Ukrainian lives should be thrown away, as if they have no value. Just used and thrown away. For your proxy war? How does that help Americans? How does any of this help?”
Mr Crenshaw’s response was simple.
“Still going after that slot on Russia Today huh?” he said.
The two have clashed in the past, going back to when Ms Greene first won election to Congress. Earlier this year, Mr Crenshaw said in an Instagram post that she was either “ a Democrat – or just an idiot.”