Had a look at the live page - clearly it's already utilizing CSS. You need to remove the border property from a couple of rules to get the look I think you're after.
Have a look inside style.css, you want to make changes to the following rules:
Line numbers given by Chrome - they may/may not be accurate.
Just remove or comment out /* excluded_rule here */ any reference to border in the below styles.
style.css - line 639
.entry img, img.thumbnail {
padding: 5px;
border: 1px solid #E6E6E6;
background: #F8F8F8;
}
style.css - line 1224
table {
border: 1px solid #E6E6E6;
border-right: 0;
border-bottom: 0;
width: 100%;
border-collapse: separate;
margin-bottom: 1em;
}
style.css - line 1225
table td, table th {
border-right: 1px solid #E6E6E6;
border-bottom: 1px solid #E6E6E6;
padding: 4px 8px;
vertical-align: top;
}