Pros don’t waste their time with the Magic Eraser or the Extract Command. Instead they turn to layer masks, which give you ultimate control over removing elements from an image (plus they maintain the ability to get content back again).
1. You create a layer mask by clicking Add Layer Mask at the bottom of the Layer palette. If you have a selection before clicking the button, Photoshop will use this and add an initial mask.
2. With the layer mask selected (look for a mask icon, not a brush next to the eyeball), you can use the brush tool to paint black into the layer mask. Everywhere you paint, you will see your image in that layer disappear.
3. The good news is, if you want something back, switch to white and paint it back in. A very useful set of keyboard shortcuts can be learned by the pneumonic devil’s xylophone. D loads the default colors of black and white, X toggles between those colors.
There is really no reason to destructively edit your layers with this powerful technique. You can take this a step further by unlocking the mask from the layer content and positioning the mask independent of the image to place it exactly where you want it.