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.
This is what I get when I log in on swtor.com My account name is DoitbigTFC on the swtor website that I login with
Sswtor CS here will be on soon, but apart from trying a different web browser to see if the link appears
If it doesnt appear CS need to remove the key manually
Just to confirm it was swtor CS per the numbers at this link and not EA CS as they cant remove a security key
The number on the page you linked me was the number that I called. If CS did not perform it correctly, it must have just been miscommunication. The associate was very nice and understanding, but it was hard to hear him, and although he repeated my log in name about 5 times, it was hard to know if he actually said it correctly.
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.
