give the modify button an id:
<input id="Modify" type="image" alt="Modify information" value="Modify information" src="WA_eCart/Images/Nautica/Btn4_EN_modifyinformation.gif" class="eC_ImageButton" onclick="document.location.href='plugins/checkout.php';return false;"/>
and add another statement to onclick event of the submit button to hide the modify button;
<input type="image" name="Submit_order" id="Submit_order" value="Checkout" alt="Submit order" src="WA_eCart/Images/Nautica/Btn4_EN_submitorder.gif" class="eC_ImageButton" onClick="this.style.visibility = 'hidden'; document.getElementById('Modify').style.visibility = 'hidden';" />