I'll just have them change the entry in the demonology textbook from 'almost extinct' to 'not extinct enough for Alec. He prefers his monsters really, really extinct.' Will that make you happy?

This quote is suggesting that Alec would like monsters to become even more extinct than they already are. The person speaking the quote is offering to make this happen by changing the entry in the demonology textbook to say that monsters are “not extinct enough for Alec,” instead of stating they are “almost extinct.” This would be done to make Alec happy.