Obviously he's blackmailing her about something and she's desperate to keep that truth from coming out. So what deep dark secret of dear Vedu is he holding against her?
My takes:
1) They had an out of wedlock child (ooh - then they can bring the child into the family as another person to show as a grown-up post leap, along with Vansh and Kairav)
2) Both of them planned to get her into the Goenka household as a con but she fell in love with Kartik and called it off (maybe she had him sent to jail and he has just come out)
3) She's a man - a short, eyeliner-loving, weepy man
3