It is important to be able to customize the icons that show in Tabbed Compact (or other UI) toolbars. Not every laptop has room to show all icons that are by default. Besides, not every function is needed, according to each user.
The Customize menu option doesn't provide a mean to add/delete icons from these new toolbars.
This is not a bug report, but an improvement request.
Thanks for filing, this has already been addressed. Improvement available at 22.214.171.124 and master/6.5.0.
*** This bug has been marked as a duplicate of bug 101513 ***