the secretary made a note of it in case (she should forget.)

目测应该是的,参考资料如下：
should用于if引导的虚拟条件句中
在表示与现在或将来事实相反的非真实条件句中,谓语动词形式可用“should + do”.如：
If she should refuse,they could be greatly disappointed.
【考例】 This printer is of good quality.If it _______ break down within the first year,we would repair it at our expense.（2009年,天津）
A.would B.should
C.could D.might

对，是的！

连接词“in case可以用来引导虚拟语气，其形式通常为：“…in case + 主语 + should + 动词原形”。 其中should 通常不省去。
He took his coat with him in case it should rain.
他带着雨衣以防下雨。



如题时表示对将来的虚拟，另外，in case 不一定都...