Final answer:
The housekeeper likely thinks the apparition is Peter Quint due to the psychological impact of the house's history and the mysterious, intangible influences that have been suggested to linger in the space.
Step-by-step explanation:
The housekeeper concludes that the apparition is that of Peter Quint because of the suggestive power of the surroundings: the historical memories and tales presumably absorbed from the house's old walls, whispers among the servants, and the very atmosphere imbued with past treacheries as hinted by the narratives. This idea is mysterious or strange because it suggests an unseen influence or psychological hypnosis on those living in the house, implying that the ghosts or memories of the past are powerful enough to manifest as visions or perceptions to the current inhabitants of the house, and specifically, to the housekeeper.
This strange occurrence is amplified by the historical context of the house, Dare's Gift, and the weight of its past events, as represented by Drayton's musings on the everlasting impact of ideas beyond the physical acts. It suggests that the phantom of Peter Quint is not just a simple ghost story but a complex psychological phenomenon that continues to reverberate through generations, posing eerie questions about the boundaries between what is seen and unseen, tangible and intangible.