If you would like to do quick checks of different domains, the way to go would be the on-demand backlink checker.
It's how you can quickly do checks on any domain. Each check uses up 1 credit. Premium plans come with a monthly credit allowance, and if you run out you can purchase more.
You can access the backlink checker by:
- clicking on the Tools icon
- clicking on "Free Backlink Checker"
Once you do that, If you are on a paid plan, make sure you click on "On Demand" so that you are using the Backlink Checker without the restrictions from the free version.