Marked for Death only gains an extra die for attacks from creatures.
So, it will not gain a die for a wall Bash attack. It will not gain a die for direct damage, such as the Burn condition or the Ghoul Rot enchantment. It will not gain a die for attacks from Conjurations, such as The Temple of Light or the new Akiro's Hammer.
The damage barrier is unique situation. It is not considered an attack coming from the creature it surrounds. It is a special type of automatic attack, which is attached to the creature, but does not originate from the creature. Thus it gains no bonus from Marked for Death.
On tough calls like this, we try as much as possible to rule in favor of what makes the most sense, what is realistic, and what is the intent of the spell. The damage barrier is an unintelligent, automatic attack attached to a creature. It also does not gain any bonuses from the creature it is attached to, because the attack is not considered to originate from the creature.