Many of the handles in my house are of this variety - a lever not a knob. My daughter has a cat that lives in our basement along with my daughter. She (the cat, not my daughter) was supposed to stay for one night, but about 5 years later she is still here. As my spouse of a few years is allergic to cats and barely tolerates my less allergenic Cornish Rexes, I have not allowed the basement cat upstairs. But that did not stop her. She learned to jump at the basement door and swat the lever, thus releasing the catch and pushing on the door to open it. Every so often I would find her wandering around the house, much to the chagrin of the upstairs cats. So we changed the handle. She still bravely launches herself at the door and swats, but unless someone has left the door ajar, which occasionally happens, her efforts are futile.
I did catch her wandering around the house the other morning. She quite enjoyed exploring and my old cats no longer seem bothered by her presence.