AN ACR LTT HIT A JETWAY WITH ITS L WINGTIP.

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WE WERE CLRED TO TAXI FROM GATE X. ANOTHER LTT WAS PARKED NEARBY TO OUR R AND AHEAD AND TO THE L OF OUR ACFT WAS THE JETWAY TO GATE Y. DUE TO THE CLOSE PROX TO THESE OBSTACLES AND SURFACE CONDITION (RAIN); WE STARTED BOTH ENGS. IN ADDITION; 1 WINGWALKER PER WING AND LEAD RAMP AGENT AT THE NOSE WERE PRESENT TO ASSIST MANEUVERING. DURING TAXI; THE FO WAS CHKING THE R SIDE OF THE ACFT AS WELL AS GUARDING THE BRAKES WITH ME; ALWAYS INDICATING THAT WE WERE CLR OF THE OTHER AIRPLANE. I WAS MONITORING THE L SIDE OF OUR ACFT AS WELL AS OBSERVING THE LEAD RAMP AGENT'S TAXI INSTRUCTIONS. THROUGHOUT THE MANEUVER; THE TAXI SPD WAS VERY; VERY SLOW AND CAUTIOUS; WITH BOTH ENGS RUNNING. AS THE JETWAY TO GATE Y APCHED; WE WERE GIVEN A TAXI-STRAIGHT-FORWARD COMMAND FROM THE LEAD AGENT. THE L WINGWALKER; STANDING IN FRONT OF THE WING AT THE WINGTIP; GAVE NO INDICATION OF THE WINGTIP-TO-OBSTACLE DISTANCE; BUT SMILED AND GAVE A THUMBS-UP; THEN WALKED UNDER THE WING AND DISAPPEARED FROM VIEW. MY ATTN SHIFTED TO THE LEAD AGENT; MARSHALLING US WITH STRAIGHT-AHEAD COMMANDS AT WHICH TIME WE FELT A SHUDDER IN THE AIRPLANE. AS WE CONTINUED AHEAD; PAST GATE Y; I ASKED THE FO ABOUT THE SHUDDER AND THEN RECEIVED THE STOP TAXI COMMAND FROM THE LEAD AGENT. THE LEAD AGENT THEN WENT TO THE L WING AND SHOOK HIS HEAD AND MADE A FACE TO INDICATE A PROB TO THE L WINGTIP AREA. AT THIS TIME; OUR ACFT WAS BEYOND GATE Y AND WE WAITED FOR THE OTHER LTT TO CLR ITS PARKING SPOT AT GATE X. THE LEAD AGENT SIGNALED WITH HIS HANDS TO RETURN BACK TO OUR PARKING AREA AT GATE X. WE TAXIED BACK TO PARKING AND SHUT DOWN THE ACFT AND VISUALLY INSPECTED THE L WINGTIP TO ASSESS THE DAMAGE.