do 2 holes at a time ...
You can also do 2 holes at a time ... leaving the door on it's hinges rather that rehanging it.
Just remove 2 of the 4 screws, drive in the tees or toothpicks if the holes are small enough, with some glue or epoxy and then break them off after it's set up. Then replace the other 2 screws. The screws at the top hinge are the issue. The weight of the hollow core door is minimal, but any pressure on the knob downward tends to pull on the top screws.
Make certain you use some longer screws that go all the way into the 2 x 4 frame, not just the casing as is normally done, IF you want a permanent repair. Pre-drill the hole for the longer screws using the body of the screw as the size for your drill.