I’m not exactly sure what you consider to be the “border” here, as such. That flag image doesn’t have a caption, for example, so that changes things a bit.
There are several places in your theme that affect the margins and border of the images on that front page.
The first area is in the theme’s style.css file starting on line 1231. It looks like this:
.entry-content img,
.wp-caption {
max-width: 98%;
height: auto;
}
.wp-caption {
max-width: 100%;
background: #eee;
border: 1px solid #ddd;
margin: 10px auto 0;
}
.entry-content .wp-caption img {
border: 1px solid #ccc;
max-width: 98.5%;
margin: 4px;
}
.wp-caption-text {
color: #5e5e5e !important;
font: normal 11px arial !important;
margin: 0 5px !important;
padding-bottom: 5px;
text-align: center;
}
That refers to a lot of various things in the page for captioned images. The 98 and 100% widths, for example, are what make the caption box slightly bigger than the image it contains. The caption box has that background color of #eee to give it that gray shade. There’s also a 1px border around both the image and the caption box itself.
If you were not using a caption, then that would not apply, and lower in the style.css, around line 1356, you’d find this:
.entry-content img,
.child-page img {
border: 4px solid #e3e3e3;
margin: 5px 0;
}
That puts a 4 px border around images with a 5 pixel margin around images.
Editing your style.css file would let you change these as you see fit, or you could use a CSS Editor like the one in Jetpack to add additional CSS rules to override those.
This is arguably a better solution than overriding those on an individual image basis, because you do it one time and you’re done. No need to change it for every image.
But if you really want that per-image change back, try this plugin:
https://wordpress.org/plugins/advanced-image-styles/
