Quins kept their hopes of the treble alive on Sunday as they defeated Sale Sharks 32-14 at Sixways Stadium to get their hands on the trophy.
"Quins now have nine weeks to do something special; they have one trophy in the bank and two to go for, so what a rugby club to be at at the moment," Greenwood told Sky Sports News.
"[Conor] O'Shea has instilled some strong virtues on which they build the club. Players can come and slot in seamlessly and they just want to play with ball in hand and don't worry about exit strategies, they are just looking for offload after offload."
Greenwood's former side continue the defence of their Aviva Premiership title next Sunday when they travel to league leaders Saracens.