Ah yes, I see your dilemma. Most interior doors, to make them light, are hollow and made from wood that's just a little thicker than paper in most places. Because of that, the screws will probably keep pulling out. The easiest fix, with the lowest projected durability, is just to rotate the handle to a point where all three holes have fresh wood beneath them. From there:
1. Hold it steady and stick a pencil in each hole to mark it.
2. Drill a tiny hole the length of the screw with a drill bit that is a little smaller than the thickness of the screw on your marks.
3. Screw your handle on without over tightening.
A better solution, if possible, depends on what that metal object I see inside the door is- and if the twist handle on the other side is still there, or needs to be there. Typically with those kinds of doors you get two matching handles, and screw them to each other through the door. That way the screws basically just hold it against vertical forces, and the handles are connected by the force of squeezing themselves instead of tugging on the fragile wood. In one-sided handle situations, typically I would recommend substituting the other handle with nuts and large metal washers to simulate the same effect, so long as it was out of sight.