What evidence is there in the text of Stevenson's Dr. Jekyll and Mr. Hyde that indicates that Enfield and Utterson have suspicions after the conversation during their walk of Dr. Jekyll and Mr. Hyde being strange?
... [Enfield] lifted up his cane and pointed.
"Did you ever remark that door?" he asked; and when his companion had replied in the affirmative, "It is connected in my mind," added he, "with a very odd story."
"I see you feel as I do," said Mr. Enfield. "Yes, it's a bad story. For my man was a fellow that nobody could have to do with, a really damnable man; and the person that drew the cheque is the very pink of the proprieties, celebrated too, ... Black-mail, I suppose; an honest man paying through the nose for some of the capers of his youth. ..."
There is textual evidence related to their walk indicating that Enfield and Utterson think Jekyll and Hyde very strange indeed. I've quoted above two significant pieces of textual evidence. They relate to (1) how Enfield feels about the evil man and the story and to (2) how both Enfield and Utterson think about the connection between the "damnable man" and the "celebrated" man.
(1) Enfield makes it clear that he feels, and rightly so, that the experience he had was of the most horrific kind of experience and that the "damnable" man perpetrating the events was the most villainous and inhuman sort of man possible. Enfield recognizes that Utterson shares the same feelings: "I see you feel as I do," said Mr. Enfield. "Yes, it's a bad story."
(2) Enfield and Utterson agree that there is probable cause to think blackmail is involved in the connection between the evil man and the celebrated man who owns the door leading into "Black-Mail House," as Enfield calls it: "Black-mail, I suppose; an honest man paying through the nose for some of the capers of his youth."
When both the feelings and thoughtful explanations of the connections are added together, clear textual evidence is provided that both Enfield and Utterson think Dr. Jekyll and Mr. Hyde strange, strangely connected, strangely behaving, strangely mysterious, and--at least for Utterson who is Jekyll's close friend--strangely troubled.