If you do not wish to see the courses you have completed that are in Moodle, you can remove yourself from it.
1) To do so, login and click on the course you want to unenrol from.
2) Scroll down or look for Administration > Course Administration then select Unenrol me from "Archive..."
Please note that you can only do this for courses that have been Archived. Also, once you have done so, you will not be able to enrol yourself back into it.