Please try any one of the below implementations based on your requirement.
1) Set the css style.
This will apply to all input controls in your page and if you have multiple textboxes, then applying this css style will make all text boxes border to disappear.
<style type="text/css">
html body .RadInput input.riTextBox {
border: none;
}
</style>
2) If you want the border to removed for specific controls then use the below javascript implementation