The Man City captain and Lioness was adjudged to have taken too long over a free-kick in the first-half of a controversial 1-1 draw in the Women's Super League.
Having already been booked earlier in the contest, referee Emily Heaslip brandished a second yellow as Greenwood took more than 20 seconds to take the free-kick.
However, the decision has been roundly condemned, not least by Arsenal legend Wright, who has long championed the women's game.
Responding on X, formerly known as Twitter, he wrote: "Embarrassing.
"They keep telling us about laws of the game but where is common sense! Why would she be wasting time??? Kmt."
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He was not the only one, as Arsenal star Beth Mead also had her say and put: "Awful decision, never time wasting."
Man City star Chloe Kelly had put the home side ahead at the Joie Stadium early on in the match in the seventh minute.
And things went from bad to worse for Gareth Taylor's side as Hemp was also given her marching orders after the break.
The England international was also handed a second yellow when she tugged back Lauren James as she looked to force an attack.
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It saw City reduced to nine players while Taylor was also given a booking for his reaction.
Man City had opened the scoring through a Chloe Kelly rocket but the forward, who was substituted just seconds before, was left gobsmacked by the second red card.
And Hemp, fresh off the pitch, had to help her into the dressing room.
Sam Matterface told talkSPORT: "It was fascinating watching Chloe Kelly walk down the tunnel with her teammate Lauren Hemp trying to console her.
"The supporters inside the stadium cannot understand what has happened."
Man City's resilience was finally broken in the 96th minute when Guro Reiten grabbed an equaliser against the team of nine, netting from close range as the home side failed to clear the ball.