I grew up in the southern Appalachians; southwest Virginia. My grandmother (b. 1899) and others of her generation used this phrase: "Hit ain't worth a pewter rinctum [rinktum?]." I always took this to mean some item of little worth, such as (I imagined) a pewter ring, or some kind of small curio. I can't come up with any other references. The new Dictionary of Smoky Mountain English doesn't include the word. However, I'm very doubtful that the mountain people in Virginia were using the word to mean "anus." Would like to hear if anyone else is familiar with this usage.