You've already selected 'blankly' as the answer, but my experience is that that the word 'cluelessly' would be more likely used in the context. The definition of "blankly" doesn't correspond to your description:
"'What do you mean?' he -ly asked."
'What do you mean?' he cluelessly (MW) asked. Here you avoid the stronger terms 'confusedly' and its ilk, and at the same time stick with simpler speaking. 'Get a clue' is often heard as figurative language.
In addition, blankly tends to suggest a visual appraisal of someone's mental state, but you aren't using it dialog, you're using as a omniscient narrator when you are describing the mental state. If in the dialog the user was speaking to the person about that person's cluelessness, blankly might be a better fit. My personal experience is that people tend to use the world blankly to describe a face or state, not a mental state per se.