Annie Proulx does write about Jack's mom offering Ennis to go up to his room, and Ennis finding the shirts in the closet. I assumed Jack's parents knew about them from the short story, not from the movie. I think it's pretty much implied Jack's parent suspected there was something different about his son and that Ennis might be part of the reason. They also knew he took the shirts.
From the short story:
Ennis sat at the kitchen table with Jack's father. Jack's mother, stout and careful in her movements as though recovering from an operation, said "Want some coffee, don't you? Piece a cherry cake?
"Thank you Ma'am, I'll take a cup of coffee but I can't eat no cake just now.
The oldman sat silent, his hands folded on the plastic tablecloth, staring at Ennis with an angry, knowing expression...
Knowing what? How about the whole paragraph where that comes from?
The old man sat silent, his hands folded on the plastic tablecloth, staring at Ennis with an angry, knowing expression. Ennis recognized in him a not uncommon type with the hard need to be the stud duck in the pond. He couldn't see much of Jack in either one of them, took a breath.
I think that Mr. Twist was a person who prejudged people before he even got to know them. I think that if old man had never known whom Ennis Del Mar was and had seen him on the street in Lightning Flat, he would have looked at Ennis with that very same "angry, knowing expression." More than likely John C. Twist, Sr. looked at most folks that way. He was an angry man all of Jack's life. The only time that the expression, "stud duck," is used in the story is in the above quoted paragraph.
If you had never seen the movie and only read the original short story, do you think that Jack's parents would have known that Ennis was just more than just a friend of Jack's and that Ennis actually took the shirts with his mother's permission?
In the way that Annie Proulx described both Jack Twist and Ennis Del Mar, there would be no way that Jack's parents would have even known that their only child had a sexual relationship with Ennis, too. I think that someone else here posted something similar to that effect.
I really think that Jack's father, Mr. John C. Twist, Sr., really did not want to know his son very well and had his mind already made up about the boy from an early age. He might not have really liked children that much in the first place, especially when he both physically abused Jack by using a belt on him, instead of just helping him take better aim at the toilet bowl when Jack had to pee, and, in a way, sexually abused little Jack taking out his own penis and urinating all over Jack as additional punishment.
I say it was sexual abuse because the old man used his penis to punish Jack. That, in my opinion, fits the same category of emotional rape.
While Annie Proulx might say in an interview that Ennis took the shirts with permission, I really believe that her Ennis Del Mar stole his shirt back and took Jack's shirt along with it.
And, considering what kind of coat Ennis wore in the movie and the fact that it was very loose-fitting, he could have taken the shirts by either hiding them under his coat (inside of his shirt) or actually wearing them under his own shirt without Jack's folks even know it.