I never used the quick search field and there is no possibility to remove it from within eclipse as the request to be able to disable it seems to have very low priority in the dev team.
I’m watching the bug https://bugs.eclipse.org/bugs/show_bug.cgi?id=362420 from the very beginning and now someone posted the hint to remove it via css.
Open the file eclipse/plugins/org.eclipse.platform_<version>/css/e4_basestyle.css and add the following at the end of the file:
#SearchField {
visibility:hidden;
}
After that you have to restart eclipse. After that the quick search should be gone.