To wrap the text in an h4 tag would require a plugin. The tag is set in the TopicEmbed::imported_from_html method. You would need to re-open that method in a plugin to change the tag.
You can change the text content that is displayed from your site’s Admin / Customize / Text section. Search for embed.imported_from.
If you just want to make the text larger, you could try making the change with CSS. Either override the text size for all small elements on your site, or try to target the imported_from text with something like this:
.cooked hr + small {
font-size: 16px;
}