Save the offer to your Card and spend $40 or more, in one transaction, in-store only at BP by 14/7/16 to receive one $10 credit. Limited to first 40,000 Cards to register. Redeem offer up to 3 times at only American Express accepting BP locations.
AmEx Connect - https://network.americanexpress.com/connect/au/en/secure/doe…
Direct Enrolment - https://offerenroll.americanexpress.com/enroll/EnrollmentSit…
I manually registered my NAB AMEX so I'm quite sure your Westpac AMEX will work just fine, anyway just try to register it using the direct enrolment link above, you will receive an email confirmation when registered