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:
- going to the Link Checker section:
2. clicking on SEO Tools and then on "Free Backlink Checker":
Once you do that, you'll be directed to the tool. 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.
You can read more on how to quickly check the backlinks for a random domain here.