fcpx markers?

For a project Storyline, you can select the clips in the timeline you want to delete markers from and go to Mark > Markers > Delete Markers in Selection (or type control-shift-M).

For the Media in a project, in the Event Browser, you can select all the clips you want to remove markers from and do the same. Delete Markers in Selection will only be available if there are any markers.

Markers you add only in the storyline, stay in the storyline (that is: they aren't automatically added to the clip in the Event Browser). Markers you add in the Event Browser "follow" the clip into the storyline when added. If you add a clip with a Marker from the Event Browser to the storyline and delete the marker in the storyline, the original event browser marker stays in place - the storyline clip's marker is removed. Likewise, if you add a clip with a Marker into the storyline and subsequently delete the Event Browser marker, it will be removed while the marker in the storyline remains.

If you are completely removing all Markers, and they exist both in storylines, and in the Event Browser, you will have to remove these sets separately, as well as open all existing storyline with markers to remove those as well. I don't believe there is a way to delete all markers at the Library level from FCP alone (there may be some external scripts that can strip markers "globally").

In the project or in the browser? In the project go to the Timeline Index, go to Tags, select them all, and delete.