Importance of straining juice?

How important is it to strain the juices especially after using a centrifuge juicer? In fives days on the juice fast, I have lost a total of fourteen pounds. I do see signs that I am detoxing such as the coating on the tongue. I guess the issue is that I still see some pulp in my juice. I don't know if it is better to invest in just a strainer or a different type of juicer (If that makes a difference?)?