Arrange, settle, reconcile — could these words be used before "their differences"? What are the differences in meaning?
The object for the verb "arrange" is generally the intended result of the arrangement. With this in mind, "to arrange their differences" doesn't make much sense, since they're trying to get rid of their differences, not create them.
As for the other two, "reconcile" often has a somewhat amicable connotation, whereas "settle" is more neutral.
"Arrange their differences" sounds like they've made point-by-point lists of what their differences are so that they can go over them. It does not convey to me any sense that an agreement has been reached.
"Reconcile their differences" is an unusual phrasing but I think it works, giving the same meaning as "settle".
"Settle their differences" is the idiomatic expression indicating that the parties have reached a mutually satisfactory agreement.
The parties could also "resolve their differences" with the same meaning as "settle".