How do I replace a Top Image, Bottom Image, or Home Page Icon with no picture?

Go to your Update Index and click the Edit Page Settings button next to the page you would like to update.  In the pop-up window, click the Select button next to the graphic you would like to remove.  In the resulting window, click the "No Image Selection" button.

To remove ALL graphics on your Home Page, go to your Update Index and click the Site Settings tab, then click Customize Web.  On the resulting page, go to the "Select Home Page Style" section and choose Text Only.  Submit the update.