No. DHS will be able to communicate a traveler s ESTA status to the carriers. However, DHS recommends that travelers print out the travel authorization application response in order to maintain a record of their traveler authorization application number and to have confirmation of their ESTA status.
U.S. regulation does NOT require a Visa Waiver Program (VWP) traveler to present a printed copy of the ESTA authorization page in order to travel. However, it is recommended that you print a copy for your records. If you applied for ESTA and you have forgotten your application number, you may retrieve the application through the website by entering the applicants name, date of birth, passport number and passport issuing country.