POP3 does not normally store emails on the server after they are downloaded, however the iPad's default settings leaves emails on the server, and simply marks them read. I'm not sure what the trigger is, but Mail can forget what emails it has read, and download them all again.
This is a compromise settings so that you can use the same account on more than one device or computer. One of those devices should be set to delete emails after they have been downloaded, so they don't accumulate on the server. If all you ever use for the email is the iPad, you can set it to delete emails in the Advanced part of that account's settings. I can't tell you exactly where, because I don't currently have a POP3 account to look at.
You should double check your Centurylink support pages to see if they offer an IMAP setup instead.
At the very least there should be a webmail site you can go to and permanently delete your older emails. Then delete and re-add your account on the iPad; starting it over with a clean slate.
I always recommend getting at least one email account that is not dependent on your ISP (Internet Service Provider), for a several reasons.
1) For some stupid reason most ISP's still use POP3, which is a lot more trouble to manage on more than one computer or mobile device.
2) Sometimes have to change ISP, and it's a pain to have to change your email account and tell everyone about it.
3) Most third party email accounts (Yahoo, GMail, Hotmail, iCloud) are IMAP, or at least Exchange accounts. These accounts are far more flexible, allowing the creation and management of folders that stay synced on all devices and computers.