A B727 FLC HAD THE RADOME DAMAGED BY THE TUG'S DOOR DURING PUSHBACK FROM YYZ.

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ON PUSH OUT FROM GATE; I HEARD A CRUNCHING TEARING SOUND. TURNED OUT TO BE TUG DOOR BECOMING WEDGED UNDER RADAR NOSE CONE; CAVING IT IN AND TEARING A 12 INCH GASH IN DOME. TOLD THE DOOR CAME LOOSE DUE TO JETBLAST. THEY HAD TO REMOVE TUG DOOR TO REPOS ACFT TO GATE. INSPECTED AND FOUND SIGNIFICANT DAMAGE. CONFERRED WITH MAINT AND DISPATCH. NOT AWARE OF ANY NEGLIGENCE ON ANYONE'S PART. SUPPLEMENTAL INFO FROM ACN 446626: UPON ARR AT XYZ CLRED BY RAMP TO TAXI IN VIA LINE 3. AFTER ENTERING RAMP FOR GATE WE NOTICED X STARTING ITS PUSHBACK. THEIR PUSH WAS STOPPED AND THEIR GND CREW MOVED OVER AND PARKED OUR FLT. THEY THEN IMMEDIATELY RETURNED TO COMPLETE FLT X PUSHBACK. AS WE SAT AT THE GATE; OUR L ENG REMAINED RUNNING AT IDLE PWR DUE TO THE FACT THAT OUR APU WAS PLACARDED INOP AND WE HAD NOT BEEN PLUGGED WITH EXTERNAL PWR. AFTER WE WERE CONNECTED WITH EXTERNAL PWR; WE SHUT DOWN THE L ENG AND COMPLETED THE PARKING CHKLIST. WE THEN PROCEEDED TO BEGIN OUR DUTIES FOR OUR RETURN LEG TO ORD. AFTER OBTAINING OUR FLT PLAN FROM OPS; I RETURNED TO OUR PLANE AND NOTICED THAT X WAS STILL IN THE ALLEY WITH A TUG ATTACHED. THEIR ACFT HAD BEEN DAMAGED DURING PUSHBACK BY THEIR TUG DOOR. AN 18 INCH GASH WAS MADE IN THEIR RADOME. I WAS QUESTIONED ABOUT WHETHER OUR ENG HAD CAUSED THEIR TUG DOOR TO BLOW OPEN. (QUESTIONED BY GND PERSONNEL -- NOT FLC.) OUR ENG WAS AT IDLE PWR THE ENTIRE TIME IT WAS RUNNING AT THE GATE AND WAS NEVER POINTED ANYWHERE NEAR THEIR DIRECTION. (AS YOU COULD SEE LOOKING AT THE RAMP LAYOUT.) I CANNOT BELIEVE OUR EXHAUST HAD ANYTHING TO DO WITH THIS INCIDENT.