The seller for these cards has several Piedmont 350's listed as original, all with red backs, and no factory number. There is also at least one PD350-460, with no factory number. Each looks to have been purposely aged, and the area where the factory number would be, and the designation of reprint, rubbed off.
I contacted the seller, but wanted to put this out there in case anyone has any contacts at eBay to get the listing removed or relisted a reprints.
https://www.ebay.com/itm/1909-11-T-2...oAAOSw8zdaA3TG
https://www.ebay.com/itm/1909-11-T-2...gAAOSwvTpaAJ~8