Others have given you ways to filter them out, but let me put in a plug for why they are that way. You said yourself that the project isn't "finished" -- that is exactly why it's still visible.
So I would offer another alternative, which is simply to name (and think of) your projects differently. If you make the project task itself the "finish up" action for the project, then it makes more sense to have it in the view. For example,
Instead of this, where you are left with a task (Paint the house) that is somewhat done but ambiguous:
Paint the house
Buy paint
Power wash
Apply paint
You could try something like this:
"Finish house painting and clean up" (project name)
Buy paint
Power wash
Paint the house
Or even:
"What needs to be done for house painting?"
Buy paint
Power wash
Paint the house
Clean up
Then, when the subtasks are finished you have an explicit task which you can postpone with start date, add more children and postpone those children with a start date, etc.