The chaos that has engulfed Twickenham has so far seen Martyn Thomas resign as chairman and John Steele removed as chief executive.
Chief disciplinary officer Judge Jeff Blackett is also considering his position after being threatened with legal action should his damning report into last month's sacking of Steele be published.
Greenwood believes that efforts by the RFU to drive up declining participation numbers in the sport are being undermined by recent events.
"I'm hoping that the powers that be can get round the table and iron this one out," said the ambassador for the J.P Morgan Premiership Rugby 7s Series.
"We seem to turn corners every third year, only to then reverse back round them at a high speed of knots.
"We keep putting ourselves in a position that is a little awkward and that doesn't reflect well on the game.
"It's disappointing in terms of growing rugby as a sport.
"If we want people to be involved in rugby, we must get our own house in order."
Greenwood, however, insists the crisis will have no impact on England's preparations for this autumn's World Cup.
"The likes of Dylan Hartley, Ben Foden and Chris Ashton won't be concerned by what's happening in the corridors of power. Their only focus is the World Cup," he said.
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