There's something I don't quite get.
She says the white tulip is the other girl's favorite flower, right? Text literally says "her favorite white tulips" are embroidered on the handkerchief.
Okay then questions:
First, why is her favorite flower one that means breaking up????
Second, why does she assumes that the hanky with the white tulip means her gf doesn't love her anymore, instead of assuming her gf wants to make her happy by giving her something with her fav flower on it? Maybe I'm missing some point but it doesn't seem to make sense.