Hello Peter,
There is currently no settings to disable category avatar but you can edit the theme files and remove these avatars if you want. For instance, on the forums layout, you can edit the file /components/com_easydiscuss/themes/wireframe/forums/default.php and remove the codes below:
[gist]
<div class="o-flag__image o-flag--top">
<a class="o-avatar o-avatar--md" href="<?php echo EDR::getForumsRoute($thread->category->id); ?>">
<img src="<?php echo $thread->category->getAvatar();?>" alt="<?php echo $this->html('string.escape', $thread->category->getTitle());?>" width="24" class="t-lg-mr--sm"/>
</a>
</div>
[/gist]