I "love" how everyone in the comments is instantly thinking of blackmail stuff or worse. Keep this up and you will end up as judgmental misfits in no time. Most humans don't engage in blackmail for stupid reasons and most won't fall for it if the stakes are not very high. And the stake here, their relationship becoming known is kinda bad but no one can do anything much about it. So a blackmail working here is stupid.
But I guess it's also the fault of these common plots in mass produced manga. A good story would at least make the circumstances believable. This is not at the level of suspension of disbelief 😂