After a bit of googling I have learned that I can do the following

Delete[domains, Position[domains, "aa.com"]]

However, I think this only works if the element exactly matches the pattern, so my revised question is how would I search for a substring within an element. In effect I want to do something like this

Position[domains, StringMatchQ[#, "aa.com"] &]

But I can't quite work out how to do this.

domains = {"aa.com", "bb.com", "aa.edu", "baa.com", "cc.bla"}
DeleteCases[domains, _?(StringContainsQ[#, "aa.com"] &)]

If you have a list of names that you want to delete

domains = {"aa.com", "bb.com", "aa.edu", "baa.com", "cc.bla"};
deletes = {"aa.com", "cc.bla"};
DeleteCases[domains, Alternatives @@ deletes]
(* {"bb.com", "aa.edu", "baa.com"} *)

Hi Michael, _?(StringContainsQ[#, "aa.com"] &) Seems to do exactly what I need. However, I am not entirely clear how it works. The help seems to suggest that _?() means match any expression and then return true if the expression in the parenthesis evaluates to true. Have I understood that correctly?

Cheers Andy