Just my opinion:
No need to have them host that image so you have to connect to their server every time someone views it. Go to the site where you made the .gif and view it. Right click on the .gif and save the image to your desktop. Upload your image to your own site and insert it wherever you like. Now it’s on your server, not a third party.
If you don’t want to do that, just paste their generated/provided code somewhere on your blog:
<a href="https://www.makeagif.com/T5CpmO" title="Make Animated Gifs Online"><img src="https://www.makeagif.com/media/12-10-2010/T5CpmO.gif" alt="Gif Created on Make A Gif" /></a>
…and it appears. You just have to remember, every time it’s displayed, it’s being called from their server, not yours.