、。
That cold, curt way you answered — don't you think it's rude to the other person?
Literal
Wood [with-で] nose [object-を] tied that reply [possessive-の] way, other [to-に] impolite [quotative-と] not-think [rhetorical-のかね].
Centred on the vivid idiom 木で鼻をくくる ('to tie one's nose with a stick of wood'), meaning to give a curt, dismissive, cold reply — as if too bothered even to use a handkerchief. The sentence's topic is then その返事の仕方 ('that manner of reply'), left particle-less as an appositive. The ending 思わんのかね (plain, rough 思わないのか + emphatic ね) is an old-fashioned, slightly gruff rhetorical question — 'don't you think so?' with a taste of male speech.