Are you using a burr grinder? That should prevent any grounds getting through with a coarse setting. All of the grounds would be the same size, and too large to make it through.

Mine isn't insulated. I just pour the coffee into a thermos after pressing it. The coffee snobs say it's better not to steep the grounds longer than around five minutes or so anyway because it allegedly increases bitterness for people who are genetically unlucky enough for coffee to taste bitter at all.

But not coyotes, unfortunately.