What does "should + have + pp" mean?

" I have trouble to understand the following sentence:"
, I have trouble UNDERSTANDING the following sentence:

We sometimes use 'should' to express surprise or regret about something that happened:

"I’m amazed that he should have done something so stupid." : = He did 'something stupid' and I am surprised that he did.
“It is strange that a clever person like you should have believed him.” = 'you' believed 'him', and I am surprised, because 'you' are a clever person and YOU SHOULD HAVE REALISED he was lying/being deceitful.

They believed him. (But the other person considers they were unwise to do so).

This is a past modal and here is used to convey the idea that something wasn't a good idea, but it happened anyway. ( I should have known better with a girl like you ...)

That's a British usage. In American English, we would be more likely to say "would have believed him". It means basically the same as "It is strange that you believed him".