Word for deliberately taking the literal rather than implied message

What is the word for understanding someones implied meaning, but being completely pretentious about it and taking their words for what they literally said?

"fake or disingenuous literal-mindedness" as FumbleFingers has mentioned in his comment, seems to be the phrase you're looking for.

literal-mindedness (noun) the quality or state of tending to take words in their literal sense. Collins

"Most children under the age of five are naturally literal-minded. It takes a crafty adult to fake literal-mindedness."

A related word which ODO and OED define as

Annoyingly unperceptive or slow to understand; stupid; insensitive. Also, of a remark, action, etc.: exhibiting dullness, stupidity or insensitivity; clumsy, unsubtle.

is obtuse.

So when one is deliberately unperceptive, or deliberately clumsy or unsubtle, one is being deliberately obtuse.