Read MoreNew Cuba rules no beach bonanza for US travelers
The new regulations for travel between the U.S. and Cuba came into effect on Friday and allow Americans to spend up to $8,000 per year in Cuba and carry up to $10,000 into the island, according to a Reuters report. The regulations also permit the use of U.S. credit and debit cards in Cuba.
Harford also discussed the hits travel sites have taken since the Swiss National Bank tossed away its currency cap on the euro, leading to a surge by the Swiss franc. "Businesses that have greater exposure to Europe may be impacted by the fact that those euros translate into a lower rate," he said.
Read MoreSwiss franc shock ups ECB guessing game: Strategists
Harford added that Orbitz is actually benefiting from the euro's fall, since most of the company's business comes from U.S. consumers. "Just over 70 percent of our revenues come from the U.S., so as you see a strengthening dollar, that's actually great for the majority of our travelers because it makes Europe as a destination significantly more affordable," he said.