cwmills,
The problem widget are is not the “Recent Posts” widget, but the “GAW Miners” text widget above it.
Since you only have an image link on that text widget and the link itself is not surrounded by any div element it seems the height for the widget area is been set automatically and it does not match the height of the image.
This could be fixed easily by defining a height for the wrapping element. You could replace the contents in the text widget with this:
<a href="https://gawminers.go2cloud.org/aff_c?offer_id=34&aff_id=746&file_id=98" target="_blank" style="display: block; height: 250px;">
<img src="https://media.go2speed.org/brand/files/gawminers/34/20140807150227-300x250new.png" width="300" height="250" border="0">
</a>
<img src="https://gawminers.go2cloud.org/aff_i?offer_id=34&file_id=98&aff_id=746" width="1" height="1">
And add this to your CSS file:
#text-3 .textwidget { height: 250px; }
I added some inline styles to the link element in order to properly define the height, and by targeting the specific text widget with its ID (in this case #text-3) we make sure the height is only assigned to that specific text widget.
Keep in mind that if you were to paste this code on another text widget it will not work as the ID is specific to only one element.
A better approach would be to just wrap everything inside the text widget with a div tag and give it a class so the same code could be used on any text widget in the future.
For example you could paste this on the text widget, and get the same results:
<div class="gaw-miners-wrap">
<a href="https://gawminers.go2cloud.org/aff_c?offer_id=34&aff_id=746&file_id=98" target="_blank" style="display: block; height: 250px;">
<img src="https://media.go2speed.org/brand/files/gawminers/34/20140807150227-300x250new.png" width="300" height="250" border="0">
</a>
<img src="https://gawminers.go2cloud.org/aff_i?offer_id=34&file_id=98&aff_id=746" width="1" height="1">
</div>
And this to the CSS file:
.gaw-miners-wrap { height: 250px; }
In fact I suggest the second option better since it takes the same amount of work, but it is more flexible in that this code will work on any text widget you place it in.
I hope this helps!