put the lid on
Also, keep the lid on. Suppress, as in I don't know how but we'll have to put the lid on that rumor about her, or Let's keep the lid on our suspicions. The word lid here is used in the sense of “a cover for a container.” [Early 1900s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.