B757 Captain is informed of leading edge slat skin delamination climbing out of FL190 by a Flight Attendant relaying information provided by a dead heading pilot. Flight continues to destination for an uneventful landing.

Narrative

We started takeoff roll; rotated normally and climbed to 5;000; retracting flaps on schedule. ATC cleared us to turn right direct ZZZ and climb and maintain FL230. At or about FL190 we received a call from the Flight Attendant that a passenger seated at the right wing saw an object fall off the wing at take off. Trying to decided and validate information with the Flight Attendant we were informed that the passenger seated directly behind was a deadheading pilot. Meanwhile we were cleared to FL360 but we decided to stop at FL320 and start the process of information gathering; validation;and coordination. We notified ATC we need a lower altitude to work on an aircraft issue. We were advised to keep ATC in the loop. At that point we received a note from the dead heading crew member that we had a delamination problem on the right wing slat and it appeared that a 12 inch section was missing and some paint debris was flapping. We discussed the issue and decided to send the First Officer back to verify the problem. There was no flight control; maneuverability issues or vibration in yoke; or any unusual offset in trim which would have indicated that we had any aircraft control issues. The First Officer returned to the cockpit and informed me of the slat delamination problem. At that point we notified Dispatch; Maintenance; and Operations of the issues and requested conference with all to discuss. At that point ATC cleared us direct to a fix to cross at or above 14000 cleared to destination on the arrival. In our descent we slowed to 280 knots and discussed that if we had any significant additional delamination issue it would be at slat extension. So we prepared to continue to slow and stay clean as long as possible to reduce any possible additional delamination issues. Cleared for the visual approach. The approach landing and taxi were all uneventful in every phase of flight. The aircraft did not show or register any flight control issues during the above phases of flight. After deplaning we were met by station personnel and maintenance pursuant to our conversations. I had the chance to actually to see the damage first hand. Which I confirmed was significant after slat extension. I have never seen that type of delamination in my 23 years at this company. At no point was there ever a flight control issue; vibration; or a controllability issue.