A "Puller Prush Person" is in reality a Fuller Brush Person.
Years ago, employees (called distributors) of the Fuller Brush Company went door-to-door selling brushes and other useful household items to homemakers (aka housewives). I remember my mother buying such items as potato scrubbers and hair brushes from the Fuller Brush man (sorry, ladies, probably 99 percent of the salespeople were men back then, and, I might add, the term housewife was neither an epithet nor pejorative label).
Obviously, the woman in your excerpt who answered the door was mispronouncing Fuller Brush Person. For some reason, it came out Puller Prush Person. Perhaps the mispronunciation was the author's way of injecting some humor into the story.**
For more information about the Fuller Brush company, there is the following article taken from here.
Hartford’s Fuller Brush Company Goes Door-to-Door Across US
Founded in 1906 by Alfred C. Fuller, the Fuller Brush Company was one of Connecticut’s most notable corporations. Fuller developed both its original products and its iconic door-to-door sales force. In his first year, with an investment of $375, Fuller moved his one-man shop from his sister’s basement to Hartford. There, he set up shop as the Capitol Brush Company in a Park Street building that he rented for $8 a month. He renamed his enterprise the Fuller Brush Company in 1913.
From One-Man Shop to National Corporation
In its first year, the fledgling company offered 32 different types of brushes, mops, and brooms. By 1908, it also had a new employee. Fuller’s wife Evelyn became one of the first Fuller Brush representatives—and she outsold him her first day on the job and nearly every day thereafter for two years. In 1909 the business became a national corporation after an ad for sales distributors in the Syracuse Post-Standard yielded 260 dealers. These door-to-door salespeople received no base salary, walked an average of six miles per day, and sold to only one of every five homes. According to archival documents from the Fuller Brush Company, seven out of ten recruits failed in the first three months.
The Fuller Brush plant in East Hartford, 1960 – The Fuller Brush plant in East Hartford, 1960 – Hartford Public Library, Hartford History Center, Hartford Times
The “Fuller Brush Man” Becomes an Icon
During the next 20 years, company sales grew from $87,000 in 1916 to $15 million in 1923; the number of distributors increased to more than 1,000. World War I created a demand for specialized brushes that Fuller supplied to the military, and, on the home front, the Fuller “Handy Brush” was developed as a door-opening gift. By the mid-1920s, the Fuller Brush Company had an established national identity. Fuller products were sold to President Franklin D. Roosevelt at his home in Hyde Park and to John D. Rockefeller at Pocantico Hills. In 1922 The Saturday Evening Post coined the phrase “Fuller Brush Man,” and in following years, this iconic character of American life appeared in such comic strips as Blondie, Mutt and Jeff, and Mickey Mouse. Even the Walt Disney film The Three Little Pigs included a scene in which the wolf poses as a Fuller Brush Man.
Fuller’s oldest son, Howard, joined the company in 1942 and became its president in 1943. He modernized its manufacturing operations, expanded the product line to include household cleaners, vitamins, and cosmetics. He also introduced a female sales force known as the Fullerettes. By 1956 the company had 7,000 full-time distributors who visited 90% of American homes and a company catalog that reached approximately 5 million people. In 1959, the company, which had expanded and consolidated a few times within the city of Hartford, moved to a new factory in East Hartford. In 1960 sales reached $109 million, and in 1968 the company was sold to Consolidated Foods Corporation, later called The Sara Lee Corporation. In 1972 Sara Lee constructed a 600,000-square-foot facility near Great Bend, Kansas, and the Fuller Brush Company left Connecticut. The Kansas plant remains its manufacturing, distribution, and operating center.
**Thanks to user888379, Cascabel, and Fattie (see their comments below my answer), I now know that L'Engle wrote the work--from which "Puller Prush Person" comes--from an other-worldly perspective--an alternate reality.