It’s an offer they can refuse.

Carnival Corp. is pitching a tasteless “30 percent discount on future cruises” to survivors of its deadly Costa Concordia shipwreck off the Italian coast, in an apparent bid to stave off lawsuits.

The tactless move by Costa Cruises, a subsidiary of Carnival, came as rescuers pulled a 13th body from the crashed cruise liner, reports surfaced of possibly unaccounted-for stowaways killed in the disaster — and investigators hunted for a laptop computer hurriedly discarded by the disgraced ship captain.

Prosecutors believe there may be important data on the computer because of the “haste” with which Capt. Francesco Schettino gave it to a woman — believed to be a lawyer — after he hopped aboard a lifeboat carrying it in a bright plastic bag, according to the Italian newspaper La Repubblica.

Over the past week, representatives of Carnival have been phoning European survivors pushing the cruise-line discount while also asking them if they’ve been suffering from nightmares or sleepless nights, the London Sunday Telegraph reported.

“The company is not only going to refund everybody, but they will offer a 30 percent discount on future cruises if they want to stay loyal to the company,” a company spokesman said.

Brian Aho, a Schenectady resident who survived the disaster with his wife and teenage daughter with little more than their evening clothes, called the offer “kind of insulting.”

The death toll from the Jan. 13 accident was raised to 13 yesterday with the removal of an unidentified woman’s body from the sinking ship. The missing count now stands at 19, including a retired American couple from Minnesota.

The most recent victim found was wearing a life vest and discovered in the rear of a submerged portion of the ship, which is resting precariously on a reef off the coast of the island of Giglio.

Meanwhile, officials warned that there could have been more than the official 4,200 on board the cruise liner. “There could have been ‘X’ persons who we don’t know about who were inside, who were clandestine,” said Franco Gabrielli, the official in charge of the rescue efforts.

But a Concordia officer insisted it would be impossible to sneak aboard.

More attention also fell on Capt. Schettino, who is under house arrest for manslaughter and abandoning ship.

Schettino told investigators that the ship’s “black box” stopped working two weeks before the accident. He claimed that it would have recorded conversations proving that he planned to steam so close to Giglio only as a “salute” to the island in a corporate-approved publicity stunt — a claim Costa Cruises and maritime officials call false.

Schettino actions were further documented yesterday with the release of the Giglio harbor master’s official log book. It shows how Concordia crew initially downplayed the accident as a power outage and Schettino refused orders to return to the crippled ship to coordinate the evacuation.

Meanwhile, there was more bad publicity for Carnival.

A crew member on Cunard, another division of Carnival, is being probed for allegedly molesting child passengers.

The unidentified man worked for five years on its flagship, Queen Mary 2, and its sister vessel, the Queens Elizabeth, the Daily Mail reported.