By scandalous I mean that (at least some of) the other characters in the drama are shocked, even outraged by the relationship. Not just mildly forbidden romance that after being revealed ends up not being that big of a deal to others. 

Some examples of this trope done right in my opinion:

  • Crash Landing on You
  • Secret 
  • The Princess's Man 
  • Sungkyunkwan Scandal  
  • Majo no Jouken (teacher/student, ML is a minor, major objection from everyone in the drama except the leads)
  • 18-sai, Niizuma, Furin Shimasu. (FL's family killed someone close to the ML, he marries her for revenge but falls in love. The other people in on the revenge plot strongly object and threaten his life)
  • Watashi no Tadashi Oniichan (ML killed FL's brother)
  • Pinocchio (adopted uncle and niece, family strongly objects to them being together)
  • Indulgence (the leads are adopted siblings, family objects)
  • Unknown (BL, MLs are adopted siblings)

The Smile Has Left Your Eyes - much of the drama revolves around the leads wanting to be together even though everyone around them (especially the FL’s guardian) tries to convince them to never see each other again

Chugakusei Nikki - FL is a teacher and ML is her student (minor). Many people, especially ML's mother are against their relationship.

+ Pinocchio
+ Smile has left your eyes

One Spring Night 
Something in the Rain

perhaps:

Crash Course in Romance (2023) [FL is an older woman with an adolescent daughter. She and her daughter's teacher - a younger and famous man -  fall. Well, they're judged a lot by mostly everyone]

Love All Play (2022) [FL and her friend used to play at a professional team. Due to circunstances, FL is accused of hurting her friend, ruining her hability to play ever again. Later on, FL falls for her friend's brother. Of course there's a lot of criticism against it 'cause it's known that FL ruined the future of ML's sister]

Lie After Lie (2020) [FL gave birth while in jale. Years later, she discovers wich person adopted her lost daughter and pretends to be someone else to make her daughter's adoptive father fall in love with her. Well, obviously at some point all this gets revealed and FL gets judged a lot for all her lies]

Now, We Are Breaking Up (2021) [Well. FL's ex died. Later on she starts to date his brother. SO, a LOT of scandal. Dating her dead ex's brother.]

Wedding Impossible (2024) [FL is engaged to 2ML. Then, she falls for his brother. Again, a LOT of scandals even more since ML and 2ML's family are rich and famous.]

Why Her? (2022) [FL's a sucessfull lawyer and a law teacher. There is a romance between her and one of her law students that is also younger ]

Hidden Love (2023) One of my favorite dramas ever. [FL falls for her older brother's best friend. Later on, both start to date and her family doesn't like 'cause they knew each other since she was a kid and his family had a rough past]

Another Miss Oh He caused a lot of trouble to her fiancé and almost ruined her life.

Kor Kerd Mai Klai Klai Ter He's her son's best friend

My Fated Boy She's a bit older, but honestly, I think the family was mostly just surprised

Ra Raerng Fai He's her family's nemesis

Step by Step thai BL. He's the boss.

Too Late to Say I Love You She's already engaged, plus they don't have the same lifestyles

Encounter She's older and his boss.