Reweaving has placed material from the medieval period into the original cloth. The sample for carbon dating was from the reweaving portion. Also, fires have deposited ‘carbon’ onto the entire cloth which must be screened for.
The fires have not had an appreciable affect on the Shroud material. There is no soot to be found from outside sources... and the chemical reaction of fire will not change the isotopic mix of the carbon atoms so it can't skew the ratio of C14 to C12 and C13.