It's referencing Facade, a procedurally generated breakup sim where you act as the catalyst for your best friend's divorce. You have a text box and you have to find the right things to say to make Trip and Grace hate each other and eventually get a divorce. Anyway, the word "melon" instantly gets you kicked out of their apartment.
Okay, Facade isn't a breakup sim, you're supposed to save their marriage, not ruin it. However, they're both massive assholes so it's more fun to ruin their lives.
it's about an old game called Façade where you visit a couple and talk to them through typing. The AI isn't that good though so when you say melons the husband thinks you're talking about his wife's breasts and kicks you out