Hello,
You will need to modify the webpart layout. The easiest way is doing that directly on the Design tab in the webpart properties where you can switch to Layout tab and create new layout. This will allow you to modify it and you can set Visibility property of the Localized label control to false like this:
<cms:LocalizedLabel DisplayColon="true" ID="lblSearch" runat="server" AssociatedControlID="txtWord" EnableViewState="false" Visible="False" />
When you save it (click OK) the label should turn invisible.
Best regards
Ondrej Vasil