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You never specified which password you are talking about. There's also a lot of ambiguity with what you mean with "delete"; uninstall or delete the folders?

Admin Tools itself only has one password which prevents access to its features, the main password. However, Admin Tools Core does NOT have this feature which is what is throwing me off. Moreover, if you uninstall Admin Tools it removes its database tables and that password would have been cleared.

I have a feeling that you are most likely to be talking about the administrator directory password protection. Please read Admin Tools for Joomla! 3 :: Administrator password protection issues (akeeba.com)

If for any reason you have miscommunicated something (e.g. what "delete" means in this context) and you were really talking about the main password please delete all records from the #__admintools_storage table — but not the table itself!

If you mean something else... well, please be more specific and possibly post some screenshots so I can understand what you're talking about and I'll be able to help you on Monday when I'm back at the office.

Edit the options of the System – Admin Tools plugin. Set up the “Delete inactive users” and “Delete after this many days” features. Their documentation is in https://www.akeeba.com/documentation/admin-tools/system-plugin.html

What happens is that you get bots trying to automatically and blindly make user registrations in case they can abuse a registered user to submit spam on your site. Of course this fails Joomla's registration validation over email, meaning this spam registrations remain deactivated. The Delete Inactive Users feature is made to delete these useless users who have never visited your site. Set the first option to “Activated or not, as long as they haven't logged in” and the second one to 7. This will give users up to 7 days to go through activation. If they fail to do that, they will be removed.