I suppose that the Authorize.net extension Accepted Cards setting is to show what payment card icons to display during checkout. But this is not working.
For now, you'd have to manually go to \tastyigniter\extensions\authorize_net_aim\views\authorize_net_aim.php and comment out the ones not in need:
<i class="fa fa-cc-visa fa-2x"></i>
<i class="fa fa-cc-mastercard fa-2x"></i>
<?php //<i class="fa fa-cc-amex fa-2x"></i> no amex?>
<i class="fa fa-cc-diners-club fa-2x"></i>
<i class="fa fa-cc-jcb fa-2x"></i>
In my case, I don't accept Amex.
Update: I also found out that in case Authorize.net returns an error that the credit card processor is not accepted, it displays a generic message that gathers the options that were selected in the admin menu by me. "We only accept Visa, Mastercard, Jcb, Diners Club"