Yes. By clicking on the "No thanks" button at the bottom of your ANZ Internet Banking screen for a particular offer, you can elect not to see that offer in ANZ Internet Banking for the present time.
However, over time you may be presented with similar offers, unless you opt out of all marketing.
Offers relating to your existing accounts make it possible for you to activate additional account features, such as upgrading to an existing credit card, increase the credit limit, redraw your loan, etc.
These options can be removed by opting out of all marketing, but this means that you will not receive promotional material from ANZ until you decide to opt back in.