The response is "Anne and Jack had had a chat on Skype".
Clarification:
To paraphrase what someone said, we can use either direct or indirect speech.
In direct speech, we mirror the statement exactly as it was made. For instance, Mary said: "I bought an umbrella".
In contrast, indirect or reported speech relays the information without quotation marks. For example, Mary mentioned she had purchased an umbrella.
In this scenario, we introduce the auxiliary verb "had" because the original phrase is in the past tense, so we must shift back one step in time.
