Not much. First, the issue Lateran IV (1215) addressed was not the “extermination” of heretics in the sense of killing them. Anti-Catholics have been confused by the use of the Latin extermino in the Council’s decree and have assumed the word means the same as the English verb “exterminate.” It does not.
For example, the (non-Catholic) Cassell’s Latin Dictionary points out that extermino is derived from ex (from or out of) and terminus (boundary). In English it has come to mean pushing beyond the boundary of life, but it doesn’t have that meaning in Latin. Cassell’s defines extermino as “to drive beyond the boundaries; hence lit[eral meaning], to drive out, expel, banish . . . transf[erred meaning] to put aside, remove.” Cassell’s does not list “kill,” “exterminate,” or any equivalent as a definition.
Thus the relevant passage of Lateran IV reads, “Catholics who take the cross and gird themselves up for the expulsion [“extermination”] of heretics shall enjoy the same indulgence and be strengthened by the same holy privilege as is granted to those who go to the aid of the holy land” (Constitution 3).