In Mockingjay, why did President Snow leave Katniss the white rose?
There are multiple instances where Suzanne Collins uses the symbolism of the white rose. The imagery surrounding the rose in this book is incredibly vivid and telling of Snow's true character. Remember, Snow masks the smell of blood from the sores in his throat with these roses in his lapel.
The roses are genetically altered, there is nothing natural about them. It is a common theme in these novels that things that are unnatural are bad (muttations, people in the capitol's skin color, makeup etc, the colors of the buildings in the capitol) and that natural things are innocent and beautiful (Rue, the various districts specialities, etc). It is interesting that Snow does not cultivate a natural flower but rather a genetically altered one that has a "perfect" scent.
It is after examining the connotations that these Roses embody that we can figure out why Snow decides to leave her a rose in her home after the bombing. In Mockingjay, Katniss returns to her home in District 12 after the bombing and while everything is in ruins, she can still smell the white rose upstairs in her old bedroom. The rose is in this case is a symbol of his power and his omnipresence. He is not just in the capitol controlling Peeta's torture, but he also is able to emotionally torture Katniss all the way out in District 13.
Snow therefore gives Katniss the rose to show her that he is still has the power to unsettle her just as he has throughout the entire triology. She still has not found safety and stability after leaving the core of Panem and living in District 13. She will not be able to find safety until Snow is done in altogether.