I am less sure Henrietta refers directly to the Musgroves' belief Lady Russell persuaded Anne not to marry Charles.
I think she is thinking of her own marriage prospects.
Strolling by the sea; Henrietta elaborates it may be a good idea for Dr Shirley to retire to Lyme. Her remarks may show an element of self-interest; a future with Charles Hayter as Uppercross rector and herself living comfortably as his wife. She wishes Lady Russell lived at Uppercross, to exert her famous influence over the old rector, to persuade him to retire.
The irony for Anne is her own hopes for marriage, far from improved, were blighted by her friend Lady Rusell's persuasive skill.
Henrietta's remark may show Lady Russell is known to take an interest in local matters, jmo.