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She's careful not to hurt other people's feelings.
Literal
She [topic-は] others [genitive-の] feelings [object-を] not-harm [so-as-ように] is-being-careful.
~ないように ('so as not to / in order not to') is the negative-purpose pattern, paired here with 気をつける ('be careful, pay attention') — a natural collocation. 損ねる ('to harm, hurt, damage') is the transitive partner of 損なう / 損ねる pair, used here for emotional damage. Note the verb takes 感情 as its object marked by を — 'harm someone's feelings.' Common alternatives: 傷つける ('hurt, wound').