HS125B CREW DEPARTED HPN AND LEARNED SEVERAL DAYS LATER THEY HAD DEPARTED ON A CLOSED RWY.

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ON APR/MON/03; OUR DUTY DAY STARTED AT XA30. WE FLEW FROM CLE-MKC-TEB-HPN-BED. WE LANDED AT TEB AND PARKED AT FBO. WE WERE SUPPOSED TO FINISH OUR DUTY DAY IN TEB. I CALLED FLT TIMES IN TO FLT MGR FOR LEG FROM MKC-TEB; EXPECTING TO BE FINISHED; BUT FLT MGR SAID WE HAD TO ASAP OVER TO HPN TO PICK UP 2 PEOPLE AND FLY THEM TO BED. SO WE RECEIVED OUR PAPERWORK (FLT RELEASE AND MANIFEST) FROM DISPATCH; PREPARED THE ACFT AND DEPARTED TO HPN. WE WERE RELEASED FROM DISPATCH ALL THE WAY THROUGH FROM TEB TO HPN TO BED. WE LANDED AT HPN AND PULLED INTO FBO. WE TAXIED IN TO FBO RAMP BEHIND COMPANY ACFT THAT HAD OUR 2 PAX. BOTH ACFT WERE PARKED AT FBO. 2 PAX DEPLANED OTHER ACFT AND BOARDED OUR ACFT. MY FO BRIEFED THE PAX AND RECEIVED OUR ATC CLRNC FROM HPN TO BED; WHILE I WENT INSIDE FBO TO CALL IN OUR FLT TIMES TO FLT MGR. AFTER RETURNING TO ACFT; WE CONTINUED OUR NORMAL CHKLISTS AND CONTINUED OUR NORMAL 'UNCTLED' ARPT OPS. WE RECEIVED OUR RELEASE FROM ATC; ANNOUNCED OUR POS AT HPN AND DEPARTED TO BED. I WAS INFORMED LATER (ON APR/TUE/03) THAT THE HPN ARPT MGR SAID HE OBSERVED THAT WE DEPARTED AT XA24; BUT THAT THE ARPT WAS CLOSED AT XA00 ACCORDING TO NOTAM. WE DID NOT HAVE ANY PROBS. IT SEEMS THAT THE PROB COULD HAVE BEEN PREVENTED BY MANY WAYS. FIRST; (WE; THE CREW) SHOULD HAVE LOOKED MORE CLOSELY AT THE NOTAMS. WE LOOKED AT THEM; BUT IN THE MIDST OF THE HURRIED OP; WE OVERLOOKED THE ARPT CLOSURE TIMES. OUR DISPATCH AND FLT MGMNT TEAMS COULD HAVE SEEN AND ALERTED US (THE CREW) OF THE NOTAM. IF THE HPN ARPT MGR IS CORRECT IN SAYING THAT HE HEARD AND OBSERVED US DEPARTING; HE COULD HAVE SPOKEN UP OVER THE RADIO AND ALERTED US (THE CREW) THAT THE ARPT WAS CLOSED. ALSO; ZNY SHOULD NOT HAVE RELEASED US WITH AN IFR CLRNC FROM HPN-TEB.