While major leaders ignored her, Lagarde was caught giving Trump such a stinging "side-eye" look that it couldn't go unnoticed, leading to genuine ridicule from the public.
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One wrote: "The shade Lagarde gives Ivanka Trump is everything.
"Look at the way Lagarde powered her sight towards Ivanka Trump - God knows what was going on in her mind when Trump began talking."
Broadcaster Jeremy Vine was among the people who commented on the video, writing: "Watch Lagarde's face when Ivanka Trump tries to get into the conversation."
Another wrote: "She's like a little kid who's trying to get on the adult table at the Thanksgiving dinner."
The chorus of disapproval was led by outspoken US Rep. Alexandra Ocasio-Cortez, who commented on Twitter that being somebody's daughter "actually isn't a career qualification".
"It hurts our diplomatic standing when the President phones it in and the world moves on. The US needs our President working the G20. Bringing a qualified diplomat couldn't hurt either."
Others say Ivanka Trump "has absolutely no place being there" with one person suggesting she's "not qualified" to discuss such topics with world leaders.
However, others have stood up for her, with many taking aim at Lagarde for not being inclusive in the group's discussion.
"Their body language is incredible. Clearly marginalising Ivanka. Backs turned, no eye contact," one said.
Another wrote: "I think that says more about Lagarde than it does about Ivanka.
"Everyone has a right to be included in a conversation don't they?!"
Trump, an adviser to her father, spoke during a special session at the G20 summit.
She said that the world economy would get a boost of up to $28 trillion by 2025 if women were on an equal economic footing, before describing improving the status of women as a "smart economic and defence policy".