The default image on the TARS widget button looks like this -

You can pick another Robot image from 10 different options like this - (See How)

But, if you still want to change this to a custom image, you can do that by making one change in the code-snippet that you copied from the Distribute section. Say you have uploaded your custom image on imgur.com at this URL: https://i.imgur.com/u94ng6n.png

near the end of the code snippet, find this part:
};</script>

and replace it with
, "img":"
https://i.imgur.com/u94ng6n.png"};</script>

Make sure you use your own image URL. That's it. Use this new code-snippet on your site and the bot widget image will be updated to your custom image.

The final code snippet would look something like this - 

<script>(function(){var js,fs,d=document,id="tars-widget-script",b="https://tars-file-upload.s3.amazonaws.com/share/";if(!d.getElementById(id)){js=d.createElement("script");js.id=id;js.type="text/javascript";js.src=b+"js/widget.js";fs=d.getElementsByTagName("script")[0];fs.parentNode.insertBefore(js,fs)}})();window.tarsSettings = {"convid":"B1UbxO", "img": "https://i.imgur.com/u94ng6n.png"};</script>

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