Are you using an extension like Alby?

If not, clearing application data should do it:

1. Visit primal.net
2. Right click on page
3. Choose "inspect"
4. Find the tabs: Elements, Console, Sources .....
5. Find the Application tab (you might need to click the >> button to see more tabs)
6. In the left section, choose "Storage" inside the Application section (after Manifest and Service Workers)
7. In the main section, find "clear site data"
8. Tick all the boxes underneath the button
9. Click the clear site data button.

If you wanted to be more surgical about it, it SEEMS like they keep all their data in "localStorage" only for now.