Green’s Dictionary of Slang

not matter a tinker’s damn v.

also ...tinker’s curse
[damn n.; for ety. see also not care a tinker’s (curse) v.]

to be of no consequence, to not matter at all.

[Aus]Sun. Times (Perth) 20 Jan. 4/7: It matter’s not a tinker’s dam / (An imprecation low).
[UK]P. MacGill Moleskin Joe 308: What’s true doesn’t matter a tinker’s damn.
[US](con. 1899) H.P. Bailey Shanghaied Out of Frisco 111: It matters not a tinker’s curse.
[US]S. King Dolores Claiborne 235: I knew that what happened the next day over on the mainland didn’t matter a tinker’s damn.