I did contact my sister and asked about the connection between her college sorority's symbolic arrow insignia and the Parker Pen arrow. She confirmed only that there has always been a rumor, to date unsubstantiated, that Mrs. Parker was a Pi Beta Phi and her husband used the arrow of her sorority as the company emblem. My sister said that she never saw any proof of it and I must have just remembered the discussion of the rumor. The following is an except from a Pi Phi newsletter on the matter.
George Safford Parker, founder of the Parker Pens Company, supposedly honored his Pi Beta Phi wife, Martha, by using a clip on his pens in the shape of an arrow. Again, we found nothing to indicate that Martha Parker was a Pi Phi or that George Parker was influenced by Pi Phi when designing his pens. In fact, it was New York artist Joseph Platt who designed the clip in 1933.
There is similar speculation about the connection with the arrow on Wrigley's gum. Also unsubstantiated as far as I can tell. /Craig
edited to add that my sister is a lawyer and as such is extremely unwilling to confirm or verify anything.

/Craig