Outlook 2013 will not work wtih the new Telus Gmail migration.

It might be the data file of the old telus account. Outlook normally does not delete the file even though you have deleted the email account. You could check that by going to "Control Panel"--"Mail -- Data files. Check the extension of the file (pst or ost) and by highlighting the file and clicking "Open file location" would take you the folder the file is located. You could also remove the file by clicking "Remove" from appearing in Outlook (if it's set as default data file, you might have to make another file default, open Outlook, close it, before you'll be able to remove it). If it's a pst file, you could always use this file to setup a new pop3 account for the new Telus.net by gmail, as it will keep all your old emails, contacts and calendar. I would not recommend deleting a pst file.

I was able to setup the telus email using both POP3 (again need to enable POP3) and IMAP after much difficulty. If you've setup "Two factor authentication", try disabling it, which will allow you to use your telus (gmail) password, otherwise you'll need the unique password.

For IMAP, have you made sure the "enable IMAP" is saved, as it's possible to miss the "SAVE" button at the bottom of the page. These are my settings (for IMAP)

under "Outgoing server": enable "My outgoing server requires authentication". Under "Advanced": select "SSL/TSL" for both incoming and outgoing server. The ports should be 993 for incoming and 465 for outgoing.