If you take a look at the page SOURCE CODE for the shipping estimator popup, you will see a few ID and CLASS elements. So in fact ANY of these can contain a style declaration.
HTML Code:
<body id="popupShippingEstimator"> (HERE YOU COULD CREATE A WHITE BACKGROUND IMAGE)
<div class="shippingEstimatorWrapper biggerText">
<div id="shippingEstimatorContent">
<div class="cartTotalsDisplay important">
<br class="clearBoth" id="stBreak" />
<div class="buttonRow forward">
<td colspan="2" class="seDisplayedAddressLabel">
<span class="seDisplayedAddressInfo">
<th scope="col" id="seProductsHeading">
<th scope="col" id="seTotalHeading">Rates
<td class="cartTotalDisplay bold">
<td class="cartTotalDisplay">