One way would be to apply a transformation to the brush itself, like so:
<TextBox>
<TextBox.Background>
<ImageBrush ImageSource="/MyApp;component/Search.ico"
AlignmentX="Right" Stretch="Uniform">
<ImageBrush.Transform>
<TransformGroup>
<TranslateTransform X="-5"/>
</TransformGroup>
</ImageBrush.Transform>
</ImageBrush>
</TextBox.Background>
</TextBox>
You could also try changing the width on the brush's Viewport
property, but since you're aligning it on the right side, that may be more complicated than it needs to be.