It now seemed sinister that no one should have come to see her in the hospital and taken the chance of being recognized. It was sinister, too, that she should never have received a letter in all that time.
I take it to mean it was sinister that no one has ever come to visit her in hospital and that she never received a single letter. Am I correct?
Yes, you're right.
You can replace should have come with came, and should never have received with never received.