We are taught that the son’s of Haman learned Torah in Bnei Braq. How can this be? Isn’t there a Mitzva to wipe out Amalek?
You are bringing up an excellent point, and let me add to your question. The Yalkut Shimoni (Shemos 267) brings from the Mechilta, that this is precisely why Dovid (see Shmuel 2 1-13) killed the Amaleki ger?
See Torah Shleima – Shemos chap. 17 pg. 275, that asks your question and he brings a number of answers. Among the answers he brings is that those who were megayer them didn’t know that they were from Amalek. He gives another answer that they were grandchildren from his daughters, and by gentiles it goes according to the father, therefore they technically weren’t from Amalek. The Chazon Ish Y:D 157-5 says a different answer, that it is only prohibited to accept them as geirim during war time, and that the situation with Dovid was considered a war situation.