At the beginning of Chapter 6, Holden says of Stradlater, who has just returned from his date with Jane Gallagher:
All he did was thank me for letting him wear my hound's-tooth.
Towards the end of Chapter 4, Holden calls the hound's-tooth by its full name.
He put on my hound's-tooth jacket.
"Jesus, now, try not to stretch it all over the place," I said.
Holden has good reason to worry about Stradlater stretching his sports jacket, since the athletic Stradlater is bigger and more muscular.
Hound's-tooth was a type of wool fabric used in suits and sports jackets in those days. The fabric, which was popular in the Fifties and Sixties, was a combination of identical dark and white rounded or oval shapes which resembled a checkered pattern except that the shapes, or checks, were very small. Young men like Holden and Stradlater did not ordinarily wear suits. At a prep school like Pencey they could wear slacks and sweaters with dress shoes to classes or to the dining hall--but no tennis shoes. They favored slacks and sports jackets for dates and other off-campus activities.
Holden's hounds tooth is a jacket.
It was used as a jacket, which Stradlater takes and uses it for a date with a girl without Holden's permission.