Some items shown on the front page can be removed by going to your Recently Viewed page and using the "Clear all" link. But that does not get rid of everything.
If you see past searches appearing under the heading "Frequently Searched by You" or "Recommended for You" on the main page, those can be displaced by doing further searches of another item.
Or you can use an ad blocker to block those page elements in your desktop browser. Most ad blockers will let you highlight almost any page element and then create a rule that will hide it.
