My MIL had a strong devotion to Padre Pio, and from what my wife has told me, at one point even had a piece of cloth of his, either from a glove or a robe or a chasuble. She passed away 12 years ago, so who knows where this item(s) is.....
I hope you can find it WW. If she was anything like my Nan, I believe she would have placed it in a special place, next to other holy items or possibly in one of her missals or prayer books. Whoever of the family has these items, probably in an attic in a dusty box of holy items and holy books that she owned, well that would be my go to place to find these special relics.
I know the feeling. Back in 1909, my grandfather, Dan O'Loughlin, visited Therese's Carmel in France, and one of her sisters gave him a lock of Therese's hair. Dan shared this story in the forward to a book of poems he published in 1946. But as to the lock of hair, no relative now knows where it is! May you be more fortunate. Therese, help WW find this precious relic!
If my wife ever gets back to Ireland, she might be able to rummage through some stuff in her old house, her brother lives there currently. She did say that a lot of things were kept in the barn outside, so I don't think that would bode well for textiles.