The 21-year-old made a loan switch to Spain on transfer deadline day after it was announced last month that he would continue his career away from Old Trafford.
Greenwood was suspended by United last year over allegations relating to a young woman after images and videos were posted online and faced charges including attempted rape and assault but the Crown Prosecution Service announced in February this year that the case had been discontinued.
On Sunday he made his first appearance for his new club, coming off the bench with 13 minutes of the LaLiga contest remaining and with the teams level at 2-2.
And The Athletic has reported that while a number of home fans cheered his introduction, some Osasuna supporters chanted “Greenwood, die”.
Osasuna coach Jogoba Arrasate was quoted by The Athletic as saying after the match when asked about the chants: “The chants of ‘F*** Osasuna’ were very bad and the chants against Greenwood were very bad too.
“He is a player who, in the end, the justice system had its say. He is a very good player. But if we talk about chants, we should talk about all the chants, not just some.”
Greenwood looked bright and he had a hand in his side’s winner, earning a corner from which Nemanja Maksimovic scored.
Earlier, Stefan Mitrovic opened the scoring for Getafe but Iker Munoz equalised just before half-time.
Jose Carmona headed in to restore the hosts’ lead in the 51st minute but Ante Budimir’s penalty six minutes later levelled things up for a second time and that was the extent of the goalscoring prior to Greenwood’s introduction.
Unused substitute Fabrizio Angileri received a red card for dissent in the closing stages but Getafe held on during 10 added minutes to seal the win and maintain their unbeaten home record.
Their next match is at high-flying Real Sociedad next Sunday.