A year after Gurney’s Inn of Montauk was featured on Travel Channel’s “Hotel Impossible,” a makeover-style show where hospitality specialist Anthony Melchiorri fixes underperforming properties, the beachfront resort is under new ownership and getting a face-lift. Real estate investors George Filopoulos and Lloyd Goldman purchased the property in June, and will renovate the oceanfront resort to include, among other things, a new beach club serving food and cocktails and DJs and entertainment on the weekends. Gurney’s Inn has been owned by the Monte family since the 1950s, and general manager Paul Monte will remain on board. Jimmy Fallon, Cameron Diaz and Naomi Watts are among the A-list visitors to Gurney’s in recent years.