great topic and you are absolutely right. the twined shirts were Jack's way of trying to hold on in some substantial physical way to what he felt for Ennis. why did he leave then at OMT's house? what if Mama Twist went on a cleaning rampage and threw them out? 20 years hanging on a nail was a long, long time.
Sure is a great topic.
Far as Mrs. Twist...maybe what she said to Ennis, that she "kept his room like it was when he was a boy and I think he appreciated it" also, and most importantly, applies to her keeping the shirts safe.
I think she knew to at least some degree what they meant, whether Jack told her in so many words or not, and she was telling Ennis that she knew.
And after he found the shirts he would have understood what she meant.
He made sure that she knew what he'd taken from Jack's room, and believed that she'd give her blessing. All under the angry, and unknowing, stare of OMT.
The shirts would be safe in Lightning Flat. I can't see OMT being bothered to set foot in Jack's room.
I can't see the shirts being safe in Childress, where there was what looked like a lot of decorating (and the inevitable throwing out of 'these old things') that goes along with it.