B737 CREW HAD XING ALT RESTR NOT MET.

Narrative

FLT WAS PROCEEDING DIRECT SIE (SEA ISLE) AT FL370 WHEN DIRECTED BY ATC TO CROSS 25 MI S OF SIE AT AND MAINTAIN FL350. MY FO AND I HEARD THE CLRNC AS 25 MI S SIE AT FL250. I (CAPT; PNF) REPEATED THE CLRNC AS I HEARD IT...'25 MI S SIE AT FL250.' SINCE THERE WAS NO CORRECTING RESPONSE FROM ATC; THE FO (PF) INITIATED A RAPID DSCNT TO FL250...THE XING RESTR WAS VERY CLOSE SO A 4000 FPM DSCNT WAS NECESSARY. PASSING APPROX FL360-FL355; I DECIDED WE WOULD NOT MAKE THE XING RESTR AT FL250 AND NOTIFIED ATC. ATC RESPONDED WITH AN AMENDED CLRNC TO SIMPLY MAINTAIN FL350. THE FO IMMEDIATELY INITIATED A CLB BACK TO FL350; BUT THE ACFT HAD ALREADY DSNDED THROUGH FL350. THE CTLR MENTIONED; AFTER THIS EVENT; IN A CASUAL VOICE; THAT WE MAY HAVE HAD A LOSS OF SEPARATION WITH ANOTHER ACFT. THIS SURPRISED US AS WE GOT NO RA OR TA; OR VECTORS FROM ATC. AFTER OUR NEXT FREQ CHANGE; WE WERE INFORMED OF THE 'LOSS OF SEPARATION' OFFICIALLY. I BELIEVE THIS SIT WOULD HAVE BEEN AVOIDED IF THE CTLR HAD RESPONDED WITH THE CORRECT CLRNC SINCE WE OBVIOUSLY MISUNDERSTOOD THE CLRNC.