This is the 957th most frequent Korean word.
했다고
"했다고" means "said (that someone) did" or "claimed (that someone) did."
Here, '했다고' is part of '잘했다고', indicating the indirect quotation or report of someone saying or acknowledging that the work was done well.
그는 일을 잘했다고 칭찬을 받았어요.
He was praised for doing his job well.
Here, '했다고' is used with '거짓말을', indicating a report or depiction of the action someone allegedly did, here in the past.
사람들이 그가 거짓말을 했다고 믿고 있어요.
People believe he lied.
In this sentence, '했다고' follows '몰랐다고', showing the function of quoting or reporting that someone said or conveyed.