Last month, United said Greenwood, 21, would leave by mutual agreement after a six-month internal investigation.
It came after charges against the player, including attempted rape and assault, were dropped in February.
Greenwood was not in Getafe's squad in Saturday's 2-1 defeat by Real Madrid.
Speaking after the La Liga game at the Bernabeu, Bordalas said: "It is too delicate a situation to trivialise this issue.
"Everybody knows what happened, the appropriate measures were taken.
"Obviously we can only talk about football, about other issues, I think, that the people and the relevant systems did what they had to do, and everybody knows how it ended - without a condemnatory sentence.
"He's a footballer of the highest level, who comes to Getafe with enormous hope. We are going to help him to recover his best level."
United said the move to Spain "enables Greenwood to begin to rebuild his career away from Manchester United".
The United academy graduate was arrested in January 2022 following allegations surrounding material which was published online.
In a statement last month, Greenwood accepted he had "made mistakes" and took his "share of responsibility", but added: "I did not do the things I was accused of."
United's statement in August said: "based on the evidence available to us, we have concluded that the material posted online did not provide a full picture and that Mason did not commit the offences in respect of which he was originally charged."
Greenwood, whose contract at Old Trafford runs until 2025, has scored 35 goals in 129 games for the club since his debut in 2019 aged 17.
He has not played for United since his arrest and in October 2022 was charged with attempted rape, controlling and coercive behaviour and assault occasioning actual bodily harm.
Following his arrest, Nike ended its sponsorship deal with Greenwood and Electronic Arts removed him from active squads on its Fifa 22 game.
After the charges were dropped in February 2023, the Crown Prosecution Service said key witnesses had withdrawn and new material had come to light, meaning there was "no longer a realistic prospect of conviction".
United then started their own internal investigation in to the player, who was previously named one of the most valuable players in Europe's top five leagues.
In announcing the result of their investigation, United said: "All those involved, including Mason, recognise the difficulties with him recommencing his career at Manchester United.
"It has therefore been mutually agreed that it would be most appropriate for him to do so away from Old Trafford."