Should can be used in that-clauses after adjectives and nouns expressing the importance of an action. (Some words for example are - important, necessary, wish, anxious, concerned, eager, essential and vital)Some Examples:
It is necessary that she should take her medicine on time.
I’m anxious that nobody should know.
It is important that one should take care of himself.
It is my wish that my children should finish college.
I am concerned that he should marry her soon.
For some verbs expressing similar ideas, this also happens especially in sentences about the past.Some Examples:
He insisted that the agreement should be sent to all.
I recommended that she should reduce her expenses.
Other structures are preferred in a less formal style.Some Examples:
It is important that she sees me when she gets home.
Was it necessary to talk to my aunt?
This use of should is unusual in American English; subjunctives may be used.Some Examples:
I recommend that he reduce his expenses.
Was it necessary that my aunt be informed?
In subordinate clauses should is also used, after words expressing personal judgments and reactions, especially to facts which are already know or have already been mentioned.Some Examples:
It’s surprising that she should show that to you.
I’m sorry you should think I did that without care.