This is an edge case really. It may exist in Joomla Articles, but a whole bunch of other weird stuff do too.

K2 is based on common sense configurations.

If you fall into an edge case, you can just utilize K2 template overriding to modify and remove the link for K2 item titles.

First off, basic K2 templating: getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates

Then you must edit category_item.php, locate where the title is output (it should be wrapped by an <a> tag), remove the <a> tag and save. Links will now be gone from the category listings.

If you need to do this for select categories, you can create a 2nd sub-template group inside your Joomla template, for K2 overrides (e.g. /templates/YOUR_TEMPLATE/html/com_k2/NoLinksForItems/category_item.php). Then head over to your categories and select the "NoLinksForItems" subtemplate to use. Done.

This is the page title and it's not linked by default. So what's the issue?

Edit: why would the page title be linked either way... (doesn't make sense)

Read this to understand K2 templating: getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates

As you said, perhaps some HTML ended up in the wrong place by your template developer.