Add a class to a href linking to image.

I am using this code to output all images attached to a post:

[Code moderated as per the Forum Rules. Please use the pastebin]

Which outputs something like this:

<a href="https://www.example.com/1.jpg" title="imagename'><img src="https://www.example.com/1.jpg" class="attachment-thumbnail"/></a>

I want to apply a class to the but I can’t figure out how.

Any ideas?