Customize new WordPress 4.4 oEmbed

Hello,

I was able to change the icon used in the embedded post by using the Site Icon in the Customizer. (Appearance > Customize > Site Identity). According to the instructions there, the image you use should be square and 512×512. I would personally recommend keeping it very simply so that it can scale down to 16×16 and still look like the object you use for your “site identity”

There isn’t a lot of ‘how to’ on this site, yet, but you can use the following hooks to also customize the way that the embed looks:

embed_head
embed_footer

New Embeds Feature in WordPress 4.4

It looks like there are more hooks and filters in the core file that you can take advantage of in your theme or plugin:

https://developer.wordpress.org/reference/files/wp-includes/embed-template.php/

Hope that helps!