Okay, I think this should work. Find the below in your CSS page. (Go to Appearance, Editor, style.css (along the right). Find the following:
.entry-header .comments-link {
margin-top: 24px;
And change 24px to a smaller number, like 5px. The bad thing is that .comments-link will also become close to the top. Hopefully that doesn’t affect anything. If it does, you can change the CSS, so it only affects .entry-header.
Hopefully this works!