I would like to suggest having two (optional to have more) close buttons, possible one red and the other green. If you click the red close button, the tab closes as per normal, but if you click the green close button, the site is tipped a predetermined amount before the tab is closed.
If the user does not have enough BAT to tip, they can choose to see an advert in the same tab they are closing so that they can collect some BAT to pass onto the website they wish to tip. This will also allow Brave to generate more income as they will be able to show more adverts without annoying the user as it is the users choice to see an additional advert.
This will highlight the tipping feature of the Brave browser (which I think is one of the best features of the browser), basically gamifying your browsing experience without adding any additional steps into the users workflow.
The more we can entice users to tip websites that produce quality content, the faster we will be able to steer the internet away from a click bait culture to that of producing quality content again.