Recently, a border has appeared around certain navigation items. How do I remove this?
You may have noticed that the headings with the boxes don't have the Simple Link filled out in the term set and the ones without the boxes do. That's how we resolved it on our environment. I understand environments may differ.
Is it a custom navigation?
It only happens on some of nodes.
You need to use the F12 developer tools to check the style used in the issue node. Remove the style which causes it from your code.