"... if you care, don't let them know,Don't give yourself away
..."to give away
- to reveal or make something known, often unintentionally; also, betray or expose someone
She gave away
her true feelings.
He gave away
This idiom is sometimes put as give oneself away
, as in If you don't want the family to know about your gambling, don't give yourself away by spending your winnings.
(The American Heritage Dictionary of Idioms)