Bestop hardtops had carpet so that is most likely what it is. The Bestop will be fine. If it matters, the Bestop will not have the rear wiper. If yours was a softop model you would not have the defrost/wiper wires and would have to install the kit to make them work on the OEMs..
2003 TJ, 33" BFG AT, 2" BL, 2" BDS spring lift, Truck Lite headlights, Homemade sunrider top.