Evidently this was to indicate that the word "phone" was a contraction.
It occurred twice in the printed text, each time with the apostrophe:
[The telephone rings] There she is now.
[Hetty hurries to 'phone but Harriet regains her supremacy.]
[Authoritatively] Wait! I can't let the telephone girl down there hear my real self. It isn't proper. [At the 'phone.] Show Mrs. Caldwell up.Now, of course, that short word "phone"
very often shows up alone,
feeling, for sure, no need to be
accompanied by an apostrophe.