come out in the wash

ジュニア向けの小説 "A Wind in the Door"(written by Madeleine L'engle) を読み始めました。
"Did Father tell you why he has to go rushing off to Brookhaven, or is it another of those top-secret classified things?"
Mrs. Murry looked down at the checked tablecloth, and at the remains of an equation which had not come out in the wash; doodling equations on anything available was a habit of which she could not break her husband. "It's not really secret. There've been several bits about it in the papers recently."
"come out in the wash" は慣用句でしょうね。辞書を見ます。
・Oxford English Dictionary: Be resolved eventually with no lasting harm.: he's not happy but he assures me it'll all come out in the wash

・Collins Dictionary: If you say that something will come out in the wash, you mean that people will eventually find out the truth about it.: This will all come out in the wash–I promise you.

・Wiktionary: Of problems or difficulties, to work out, resolve, or become understood eventually and naturally.: It may look like a huge mess now, but I expect that it will all come out in the wash as time goes on.
汚れて見えなかった服の模様が水で洗ったら見えるようになったとか、流水で砂金を選別することを想像すると意味を覚えやすそうです。