Any tailwind will affect any landing significantly. Headwind has a similar effect but tailwind is more detrimental, causing the groundspeed to be higher, resulting in a longer landing distance.
Performance calculations should have been completed well before the approach and (in most public transport operations) there are significant safety margins. The reason for needing to know the wind moments before touchdown is that it changes the length (distance) of the flare. With slightly more tailwind, the flare is much longer. Without knowing of the increased tailwind the pilot may think he has overdone the flare and try to "put the aircraft down" resulting in an abrupt arrival.
HTH.