somebody在短语里简写有点嘛？
个人意见，两者均可。所以，课本上也是不至可否的。
catch somebody's eye在中学课本中可能说是习惯用语。
但catch somebody's eyes也经常有人说。
下面是网络上的一些例句，对照一下。
She uses many mods to catch his eyes or get him to notice her.
She uses many mods to catch his eye, or get him to notice her.
这两句是一样的意思吧。
Putting effort into your looks once in a while can catch his eyes.
Do you catch his eye every time you glance at him?
下面是Harry Potter中的一个句子。
She looked over at Draco and tried to catch his eyes but he ignored her, his eyes on Laylana....
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