A co-badged card is easily recognized by the logos on the bottom right corner. If you see the Interac logo along with the logo of a competing payment brand, you own a co-badged card.
While your co-badged debit card still enables you to use Interac Debit to shop at point-of-sale and access funds at ABMs, it now uses a competing network for online payments, instead of Interac Online. This was a decision made by your financial institution. As such, inquiries about the removal of Interac Online functionality should be directed to your financial institution.
You can learn more about co-badged cards here: http://www.interac.ca/en/co-badged-cards.html