Have a look at this blog entry on MSDN. The question was about changing the size of the sizing grip manually, and I think using the ToolStrip Renderer as suggested could work for you also.
The problem I have so far, is that it removes the background color on a status label in the StatusStrip, so it's not a solution yet, but it's a start.
public MyForm()
{
InitializeComponent();
statusStrip1.Renderer = new MyRenderer();
}
private class MyRenderer : ToolStripProfessionalRenderer
{
protected override void OnRenderStatusStripSizingGrip(ToolStripRenderEventArgs e)
{
// don't draw at all
}
}