The most common and most likely answer to this crossword clue is the 4 plus 2 plus 4 letter word CALL TO MIND
I've seen this crossword clue in The Daily Telegraph
C
A
L
L
T
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M
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D
More clues leading to the result CALL TO MIND
Buddy explains!
The straight part
We know that "Remember/what visiting baby-sitters do" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case remember/what visiting baby-sitters do = call to mind.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.