If you know the username and password then resetting the password on the EA account associated with the swtor account isnt going to help.
CS should of removed the security manually over the phone
What is your swtor username ? will see if @EA_Kipling can have a look at what occurred when you called to see if this was a mis-communication.
If the username and password is correct going to www.swtor.com (not on the launcher) and you leave the security key blank then what you should see is similar per below
If this doesnt appear only CS can remove the key over the phone.
To make it clear, CS told me that If I log in from the SWTOR website that I will get what I see currently, but if I hit forgot password from the Origin client, I will get something that looks like the screenshot that you posted.
