Martin and Jacqui Clark maintain that one report was false and that another set out events that were fictional.
The authors of the unfavourable reviews published on the TripAdvisor website used pseudonyms _ dreckit Manchester and edna B London _ and the couple wanted information about their identity as they wished to sue them for defamation.
The American company, which is incorporated under the law of the state of Massachusetts, opposed the move and have not revealed the information sought.
A judge at the Court of Session in Edinburgh earlier this year rejected a move for an order seeking to disclose names, addresses and other information on the identity of the authors, upholding a plea of “no jurisdiction”.
Paul Arthurson QC said: “I conclude that the approach contended for on behalf of the petitioners (the Clarks) would require the court in turn to make a rather alarming entirely global assertion of jurisdiction.”
The couple, who run a guest house, Tigh-Na-Cheo, at Kinlochleven, Lochaber, appealed against the ruling to three judges at the court.
But Lady Paton, who heard the challenge with Lord Menzies and Lord Drummond Young, rejected the appeal.
She said: “Nothing in the respondents’ (TripAdvisor) terms and conditions suggests that the respondents have undertaken to be bound by the orders issued by a Scottish court.”
Graeme Henderson, counsel for the couple, said they had ticked the box only because they could not otherwise make progress on the website.
He argued that the Court of Session had the power to grant the order sought and that the judge who initially heard the action had erred.
But Lady Paton said: “The Scottish courts do not have jurisdiction over the respondents, who are a company incorporated under the law of the state of Massachusetts.” Their principal place of business was in the USA.
She said nothing in the TripAdvisor terms and conditions suggested that the company had undertaken to be bound by orders issued by a Scottish court.
The civil appeal judges also found the couple liable for expenses.
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