Eivor:The forges have been destroyed. No more weapons will be made here.
Soma:Well fought, Eivor. My archers and I will return to camp and await your further orders.
Soma left with her men as Eivor proceeded to her next task.
Outcome
Eivor and Soma destroyed Crawleah's supplies.
Behind the scenes
The main target of the memory appears to be the oil carts ostensibly carrying Fulke's weapon supplies. However, destroying all six of these in advance of speaking to Soma will only get the "partial burning" dialogue. All straw-roofed buildings must be burned as well to count towards "complete burning" in advance of speaking to Soma.
On occasion, the progress bar may dip back down in the "use the archers" scenario, before eventually refilling at a seemingly fixed time interval. Killing all enemy waves in rapid succession does not appear to make the bar fill faster, and their arrows will only strike the same relative section of Crawleah while the bar advances. The only solution is to outlast the waves of enemies—the last of which contains a powerful housecarl enemy—and then wait for the burning to complete.
Like the other two quests, the last one to be completed will have its closing words overwritten with the opening words of Storming the Walls.