If you say or do things indiscreetly, you say or do things that should be secret or that embarrass people.

He indiscreetly revealed his guilt and his brother’s involvement. 他不慎透露了他的罪行和他兄弟在其中的参与。

The two were chattering loudly and indiscreetly about their husbands. 她俩大声地、旁若无人地谈论着她们的丈夫。