“God said He would blot out all remembrance of Amalek. The Bible itself disproves this statement by mentioning Amalek to this day.”

In Exodus 17:14, God told Moses to "write this for a memorial in a book..." Moses did that and God preserved the Book for 5,000 years, so skeptics would know that God keeps every promise He makes. The phrase "I will utterly put out of the rememberance of Amalek from under heaven" means that he will blot them out as a nation from the earth. There are no decendants of the Amalekites on the earth. They don't exist.