From AMLopedia
cheese it was a code word for "run away." It came in handy whenever the boys were were spying on people and the target spotted them. It was once suggested that cheese it was used as a code word for acting natural, and "moe it" as a code word for run away, but this was rarely used and "cheese it" kept its meaning.
Eventually, during Ball Hittin 2000, the phrase cheese it meant "to get rid of", used in phrases such as "Cheese the bats!".
Origin
An article posted in the Jewish World Review in 2004 sheds some insight on the phrase:
- The actual fixed idiom here is simply "cheese it" (because that part of the phrase can be used alone and still keep the same meaning), so we'll leave "the cops" out of this explanation. "Cheese it" has been part of English slang since at least the mid-1800s. The word "cheese" has been used with the meaning "to put an end to" or "to stop" since at least 1812, and this is the sense which led to the idiomatic expression. Whoever began using "cheese" in that way apparently decided to "cheese it" when people asked why, though, because no one has ever determined where that sense came from or why putting an end to an action should be related to cheese. The exact origin of the phrase must be labeled unknown.