"The Undoing" star was arrested in Los Angeles after police officers caught him engaging in a sex act with prostitute Divine Brown in a car - and Hugh returned to the U.K. in disgrace, to face the music and the wrath of his then-girlfriend, Elizabeth Hurley.
But he has never forgotten one letter of support that arrived from Hollywood, and he reminded Drew about it when she interviewed him for a recent SAG-AFTRA Foundation Conversation.
"When I was arrested in 1995, I was sitting in a country house in England surrounded by the world's press," Hugh said. "(It was) a difficult time. Tricky time. And amongst the letters that came in was one from you."
But the Golden Globe nominee was slightly baffled by the actress' words of encouragement.
"You said something weird like, 'It's actually quite hot,' " he laughed.
During the interview, Hugh Grant also opened up about the challenges his family were facing during pandemic. He said his son was getting so frustrated with home schooling that he stabbed himself with a pen during a math class.
The actor decided to take his kids to Turkey, where he is about to start shooting a new movie, while schools in the U.K. remain closed during the coronavirus crisis - but things aren't going so well in the virtual classroom.
"I've rented two teenagers to come and home school them," Hugh opened up.
"Poor things, they don't know what's hit them. Ghastly. My son self-harmed himself in front of this young tutor today because he couldn't do a basic bit of arithmetic - so he stabbed himself in the face with a Biro (pen)..."
But the dad-of-five was having a great time hanging out with the kids.
"The sun is shining and I haven't seen the sun for months," the Brit added. "That's why I'm so red in the face in this Zoom (call). I keep adjusting the light thinking, 'What's happened to me?' "
"I'm here about to shoot a film. I bought my family to get them out of London lockdown and I've been wallowing around in a pool with a three year old all day."