I can not seem to remove this image without screwing up the whole webpage.

I find the code fine:

<div class="codo_cat_imgs">
   <div class="codo_cat_img" style="background-image:url('http://offgridforums.com/sites/default/assets/img/cats/bullhorn.png')">
    </div>

but removing the image makes the whole page go out of line.
Is there any way around this?

I can not seem to remove this image without screwing up the whole webpage.

I find the code fine:

<div class="codo_cat_imgs">
  <div class="codo_cat_img" style="background-image:url('http://offgridforums.com/sites/default/assets/img/cats/bullhorn.png')">
   </div>

but removing the image makes the whole page go out of line.
Is there any way around this?

You can't just delete the image you have to work with the .less to.
Open themes/default > category.less

.codo_cat_img {

        background-color: @catImgBg;
        text-align: center;
        background-size: cover;
        padding-top: 100%;
        background-repeat: no-repeat;
        background-position: center center;
}

Here you could delete this block code for the fast way. But it's just a lazy move.