Sneaking something with 目を盗む
人に見つからないように、こっそりする。
Do it secretly, so that people don't find out.
Goo Dictionary
The expression 目を盗む literally translates to “steal the eyes”, but its figurative meaning is closer to “sneak by” or “slip something past someone”. It implies doing something secretly or without being noticed, especially when attempting to hide actions from someone who is supposed to be watching or supervising.
It is often used in contexts where someone is trying to do something covertly or discreetly, often to avoid detection or punishment. It can carry a somewhat mischievous or sneaky nuance, suggesting that the person is evading notice in a subtle or underhanded way.
Written as 〜の目を盗んで, the stealthily act is done with the hope of not being found out by the person identified directly before the の.
In English, a similar phrase is to do something “behind someone’s back”. In some similar cases, you may “slip past” someone.