AN A319 CREW REFUSED THE APCH TO RWY 22 AT LGA DUE TO A TAILWIND; A GAR ENSUED.

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ATIS FOR LGA WAS ADVERTISING WINDS OF ABOUT 320 DEGS 12 KTS AND WE WERE ON AN RNAV APCH FOR RWY 22. WHEN WE GOT OVER TO TWR. HE ANNOUNCED WINDS OF ABOUT 350 DEGS 14 KTS WHICH WAS BORDERLINE LIMITING AND TOTALLY STUPID. I ASKED HIM AGAIN. AND NOW IT WS 340 DEGS 13 KTS; BUT I'M THINKING PRETTY STRONG QUARTERING TAILWIND AND A BAD IDEA. WE SAID NO TO THE APCH; BUT WERE STILL ABOUT 2000 FT. TO GET OUT OF THE APCH MODE AND GET GAR LOGIC; YOU HAVE TO ADVANCE THE THROTTLES TO TOGA AND QUICKLY SNAP THEM BACK TO 'CL' DETENT. WHILE THE FO DID THIS; WE THINK THE CTLR CLRED US TO 2000 FT IN THE MIDDLE OF THE THROTTLE UP. THE MISSED APCH ALT WAS 2700 FT; BUT WE STILL HAD 3000 FT SET IN THE WINDOW AS THAT WAS OUR INITIAL POINT OF THE APCH. WE; WITH THAT THROTTLE BURST; SHUT UP TO 2700 FT AND EVENTUALLY LEVELED AT 3000 FT -- WHICH I ASKED IF THAT WAS OK. THE TWR FELLOW SAID YES; AND THERE WAS NO CONFLICT THAT WE KNOW OF. 5 MINS LATER; THEY HAD THE ARPT TURNED AROUND; AND WE LANDED ON RWY 31. THERE WAS OBVIOUS CONFUSION CAUSED MOSTLY BY TRYING TO GET US TO LAND WITH A SERIOUS TAILWIND.