Challenger has a trait which states

A GAME FOR THE WORLD: At the beginning of the game, you may generate Pyramoid markers anywhere on the map that aren't within 4 squares of each other or a starting area. You generate 3 of them and an opponent generates 2. // When Challenger would take damage, you may instead remove a Pyramoid marker within 6 squares (and take no damage). // Opposing characters have "POWER: Remove from the game a Pyramoid marker in a square this character occupies."

If I were to pulse wave challenger would he have to take the damage or could he remove a pyramid marker?

If it doesn't say Protected: Pulse Wave, he would take damage.

Yep. Challengers biggest weakness is pulsewave. Give him Captain Americs gauntlet to solve that problem.