いらぬ告げ口をして彼らの結婚生活に波風を立てることはない。

。

There's no need to make waves in their marriage by tattling on them unnecessarily.

Literal

Unnecessary tattling do-[and-して] their marriage-life [to-に] waves [obj-を] raise thing [topic-は] not-exist.

告げ口 'tattling / telling tales' is a compound (告げる 'to tell' + 口 'mouth'). 波風を立てる 'to make waves / stir up trouble' is a set idiom (波風 'waves and wind' + 立てる 'to raise'). ことはない 'there's no need to / one need not' is a set construction negating necessity.