Hope it helps you:
1. Select the textbox and make sure that the cursor inside the textbox is not in there because if it is there, it means you are in the editing process. If it is already selected, right click it.
2. Choose Format Text Box, then a box will appear.
3. Under the Line section, choose no color in the Color field.

Shortcut if you are using office 2007
1. Select the textbox, no problem if the cursor is there.
2. Go to the last tab, Format tab on the Menu bar.
3. On the Text box styles, choose No Outline under Shape Outline.