Should and ought to + infinitive express obligation and duty. Should is used when we offer a subjective opinion, while ought to has a more general and more objective meaning:
Should in that-clauses is used as an alternative to present or past tenses to express surprise or disbelief:
I'm sorry that he should feel that way.
It's funny that we should be living in the same block of flats.
It's surprising that she should have said that.