Yes, there is a way to remove it.
I quickly hacked together a simple addon that does this via an XUL Overlay specified in its chrome.manifest. I don't see a good way to achieve this without an addon or modifying files.
The original file,
chrome/messenger/content/messenger/quickFilterBar.xul located inside
omni.ja sets the text with the following XUL tag using the attribute
emptytextbase (on line 139, for Thunderbird 24.5.0):
<textbox id="qfb-qs-textbox" flex="1"
Just for reference:
&quickFilterBar.textbox.emptyText.base; is defined in
chrome/<lang>/locale/<lang>/messenger/quickFilterBar.dtd, also located inside
The XUL Overlay inside my addon changes the text to an empty string with the following line:
<textbox id="qfb-qs-textbox" emptytextbase=""></textbox>