。
She kept a tight grip on the purse strings.
Literal
She [topic-は] wallet [genitive-の] string [object-を] firmly was-tightening.
財布のひもをしっかり締める is a parallel idiom to English 'tighten one's purse strings' — both languages reach for the same image: a money pouch closed with a drawstring, kept knotted shut. 紐 (ひも, 'string, cord') is the literal drawstring; 締める ('tighten, fasten') gives it the action. しっかり ('firmly, securely') is a 擬態語 (state mimetic) that intensifies the verb. The progressive 締めていた conveys an ongoing past state — 'was keeping it tight,' not just a single moment of tightening.