The Question and Answer section for The Scarlet Letter is a great resource to ask questions, find answers, and discuss the novel.
The stranger is Roger Chillingworth. Hester fears the small deformed man and holds Pearl close to her bosom.
The Scarlet Letter was first published in the spring of 1850.
This "attribute" refers to the physician's knowledge of science and his ability to converse.... in other words, he was referring to Chillingworth's "intellectual cultivation".