Cells

If you’re not using a Child Theme, and if the theme doesn’t have a designated section of the dashboard for CSS modifications then install this Custom CSS Manager plugin http://wordpress.org/plugins/custom-css-manager-plugin

Then use its “CSS Code” section of the dashboard to hold your CSS modifications:

Alternatively use your Child Theme style.css file to hold your CSS modifications:

table,
table tbody td {
    border: 0;
}

Clear your caching plugin’s cache and deactivate it – Don’t use caching plugins when developing your site.

That’s a bit unfair, I didn’t have that information before. I didn’t know you wanted it to work on that site too.

First look at that site’s custom CSS and spot the syntax error:

#page .container header.entry-header h1.entry-title, #page .container header.archive-header h1.archive-title {
color:#5AC1E0 !important;

Close off your style first.

Okay now that’s a different context. Please do me a favour and list out all of the different contexts of the border issue.

Add this:

.site-content .entry-content p a img,
.site-content .entry-content p img {
    box-shadow: none;
}

Add

table tbody tr:last-child td:last-child {
    border: 0;
}