「背が伸びて入らないわよね」「そう、断じて太ったわけではない！」「成長したという便利な言葉は我々の切り札」

「」「、！」「」

'You've grown taller so it doesn't fit, right?' 'Exactly — I absolutely did NOT gain weight!' 'The convenient word "grew" is our trump card.'

Literal

'Height [subject-が] grew [and-て] not-fit [feminine-わよね]' 'Right, absolutely gained-weight [it's not that-わけではない]!' 'Grew [called-という] convenient word [topic-は] our trump-card'

A three-person comedic exchange about outgrown clothes. 断じて…わけではない 'absolutely not the case that' — 断じて intensifies the denial. 切り札 'trump card' — 切り 'cut' + 札 'card.' 成長した 'grew' is the diplomatic reframing of 太った 'got fat.' The humor lies in the transparent euphemism.