I think I have something else interfering with this feature. I exited Open Shell for the current session, bringing back the old start menu and explorer windows. The ability to delete individual search strings is still not there. This may be related to something else I have done to my PC.
Look for that string in the registry, then delete that entry. Registry editing is a bit dicey.
I think you may be right about it being something else. I’ve never had the need to delete individual search terms, but I got curious, so I just poured through Open Shells advanced settings and didn’t see anything related to your goal of deleting single terms. Please follow up when you find a solution, so that I may put my curiosity to bed.