Ennis probably never saw the postcard, but that's OK because it doesn't impart any essential information. Obviously, their plans about where and when to meet have already been made.
I see Alma's reaction to the postcard as symbolic of her whole reaction to Ennis and Jack. Ripping up the postcard would be assertive, active, definitive. It would be making a move, however small, to interfere with their relationship. But she doesn't do that, to either the postcard or the men.
Instead, she lets the postcard remain but buries it where it can't be seen, just as she buries and hides her knowledge about what's going on with her husband.
We've talked about the newspaper headline "honey" overlapping with Jack saying "honey" to Lureen in the following scene. Meanwhile, Alma is burying the secret of her marriage under a false endearment that helps maintain the appearance of a happy relationship.
