Remove Content from Excerpt

Hello,

The the_excerpt() tag automatically pulls in the content from the top of the post, regardless of its formatting. I have a plugin installed that lets me add/remove html tags, but I haven’t found anything that lets me ignore content within tags.

Because each post starts with a photo, the first text content below the photo is a h2 tag. Therefore, the excerpts on the front page look something like this:

The First H2 Title Main content for the post text begins right after heading tag without any indication of what it is and why it’s there.

I would like the excerpt to remove “The First H2 Title” from the excerpt which is in the post formatted like this:

<h2>The First H2 Title</h2>

Is it possible to remove the content between the h2 tags in the excerpt? Any help is appreciated, thanks!