For individual items listed as "Recent" on the start menu or on jump lists, you can right click on them and select to remove from this list. It will remove the recent item but leave the source program on the main menu.
Otherwise you can go to the Task Bar properties and on the Start Menu tab, uncheck the "store and display..." boxes, click apply, then you can re-enable. This will globally clear things though.
Providing more efficient and detailed control over the taskbar and start menu recently-used lists, etc., is something they can hopefully add in the future.
Wherever the info for those things is stored, it's separate and distinct from the Recent Places and Recent Items folders like: %appdata%\Microsoft\Windows\Recent
I believe the following folders are tied to the jumplists and start menu recent items, but have lost my pinned items as well when I've messed with them: