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She didn't intend to hurt anyone's feelings with her words.
Literal
She [topic-は] her own words [with-で] people's feelings [object-を] harm intention [topic-は] was-not.
感情を害する ('to hurt feelings, offend') is a slightly formal/written collocation — literally 'to damage feelings.' Spoken Japanese often prefers 傷つける ('to hurt'). The structure ~つもりはなかった ('did not intend to / didn't have the intention') is the standard way to disclaim intent for an outcome. 言葉で here uses で as the means/instrument: words were the instrument by which the harm happened. Common phrasing in apologies or self-defense after an unintended slight.