In the play Trifles, Minnie actually kills her husband because he killed her bird. The bird, a canary, meant everything to Minnie, so when her husband broke its neck, she got mad and in a fit of rage, killed him.
Minnie has been the victim of domestic abuse for some time. She'd been able to put up with a lot from her abusive husband, John, but his killing of her precious pet canary proved to be the last straw. The bird was just about the only good thing Minnie had left in her life, and so its violent death at the hands of her husband tipped her over the edge.
And yet the men investigating John's death don't realize just how much the canary meant to Minnie. This helps to explain why County Attorney Henderson doesn't pay much attention to the damaged birdcage. He just assumes that the bird has flown. And when Mrs. Hale tells him that the cat must have got it, it's clear he isn't paying much attention:
(preoccupied). Is there a cat?
The very idea that Minnie could've killed her husband over a canary, a mere trifle, simply doesn't occur to the men. As Mrs. Peters says to Mrs. Hale,
My, it's a good thing the men couldn't hear us. Wouldn't they just laugh! Getting all stirred up over a little thing like a—dead canary. As if that could have anything to do with—with—wouldn't they laugh!
But Mrs. Hale isn't taking any chances. As she says under her breath,
Maybe they would—maybe they wouldn't.
In other words, the men might well laugh about the idea that a dead canary had something to do with John's death, but then again they might not. Far better not to take a chance; far better to hide the evidence from the men, even if they'd almost certainly regard it as a trifle.