Cannot add fields to tabs in entry form

I was setting up a new channel on my site. By chance, I intended to use the field group from an existing channel.

Somewhere along the line, several of the fields in the entry form toolbar started displaying “Delete” text in place of the eyeball icons, and I cannot drag these fields into any of the tabs in the entry form.

This has happened to me before several years ago, but I’m afraid I’ve forgotten how it was fixed. Tech Support’s response was that they’d never seen this before and the only thing they were able to suggest is to update the software on the off chance that it might fix the problem.

Has anyone else seen this problem and does anyone have a suggestion about how to go about fixing it that doesn’t involve updating the software, which I’m reluctant to do until I can figure out what the problem is?

EE version: 2.11.6 PHP version: 5.4