By default, text boxes have a black border around them - you can of course turn this off if you want!
Here's how to do that for any text box:
- with the text box selected, click on the second tab in the Inspector
- you'll see there's a section titled Border
- now flip the Colour switch to the Off position, as shown here:
You can also control the default setting for new text boxes in the Preferences, on the Text page, as shown here:
In fact you'll find that almost all options you can set in the Inspector can have defaults set in Preferences..