Wiktionary
not give a tinker's damn
vb. (context intransitive English) To be uninterested in something.
Usage examples of "not give a tinker's damn".
It had been Baird who had persuaded his two colleagues to act, or rather he had persuaded General Harris to act much against that officer's better judgement, and Baird frankly did not give a tinker's damn whether Colonel Arthur bloody Wellesley approved or not.
He hung up and muttered in English that he did not give a tinker's damn about Abu Auda's religious sensibilities, which were mostly humbug anyway and never prevented Abu Auda from being as devious as a snake striking its own tail when it suited him.