。
Don't 'but' me!
Literal
But [nor-も] loofah [nor-も] not-exist [feminine-わ].
でももヘチマもない is a set dismissive idiom: literally 'there's no 'but' nor loofah,' meaning 'don't give me any buts / no excuses.' ヘチマ 'loofah' is used as meaningless rhymic filler to emphatically reject the preceding objection — part of a family of [word]も[nonsense]もない set phrases (文句もヘチマもない 'no complaints whatsoever'). The final わ is the feminine emphatic.