purse string
/ˈpəː(s) strɪŋ/noun
1A string, or each of a pair of strings, which may be drawn to close the mouth of a purse; a drawstring. In later use chiefly in similative expressions.
2 Figurative. Chiefly in plural, especially in various phrases relating to the control of money, as to hold the purse strings: to control expenditure.
Origin
Late Middle English; earliest use found in The Book of Margery Kempe. From purse + string.